Update: The commerce team have put up a page on 
Creating a Custom Index which is a similar, but slightly different way of doing this
There are many scenarios where you might want to have a custom Solr (/Azure, though I will be focusing on Solr in this post) index on the Commerce Engine side of things - in our case we were storing a large number of a particular custom Entity in Commerce, which should be searchable by (a search box in) Sitecore.  If the search was on one particular field and/or an exact match on a field, it might have been quicker and easier to use managed lists, however in our case it was very much a search query (wildcard etc.) across a few different fields.
In the examples below I will refer to a dummy Entity called 
MyObject. You can replace this with the name of your custom Entity.  Obvious disclaimer: I haven't spent hours testing this code, so don't go throwing it straight into a production environment.
Solr 
core + managed-schema
Duplicate one of the existing Solr core folders (eg. 
OrdersScope) by taking its 
conf folder and copying it into a new folder called 
MyObjectsScope. 
Don't add the core to Solr yet.
In your new 
conf\managed-schema
 file swap out the specific fields for those that you want to index.  
eg. in the Orders managed-schema these are the fields under the comment 
<!-- CommerceEngine Order -->.
In the next section below (with 
<copyField ... dest="_text">), in the 
source
 attributes, put each of the fields that you want to be able to search 
from your Sitecore (/Postman) call.  This will include the field values you've specified in each 
source attribute into the field called 
_text_ (defined a couple of sections above, in the file) which is the field that the Search endpoint searches.
Once you've finished with your config modifications, add the core to Solr.
Commerce Engine 
A quick look at the ISearchPipeline 
If you open Postman, expand the 
SitecoreCommerce_DevOps collection and hit the 'Get Registered Pipelines' endpoint, you can see that the search pipeline consists of the following (without any customisations):
- Sitecore.Commerce.Plugin.Search.Azure.QueryDocumentsBlock
 
- Sitecore.Commerce.Plugin.Search.Azure.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.Plugin.Search.Solr.ParseQueryTermBlock
 
- Sitecore.Commerce.Plugin.Search.Solr.CreateFilterListForQueryBlock
 
- Sitecore.Commerce.Plugin.Search.Solr.QueryDocumentsBlock
 
- Sitecore.Commerce.Plugin.Search.Solr.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.Plugin.Search.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.Plugin.Customers.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.Plugin.Orders.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.Plugin.Catalog.ProcessDocumentSearchResultBlock
 
- Sitecore.Commerce.EntityViews.IFormatEntityViewPipeline
 
If you want to get the gist of how search works I'd recommend having a look at the 3 blocks in bold, which make use of the policies, fields, and parameters we will define below. The first builds and calls the Solr query, the second parses the Solr response, and the third formats the results a bit more generically.
If you want to modify any part of how the query is built, you will need to customise (swap out) the 
QueryDocumentsBlock (either Solr or Azure version depending on what you're using).  For example, you'll see the 
...Solr.QueryDocumentsBlock calls 
SolrContextCommand.QueryDocuments(...) which adds the 
artifactstoreid filter to your Solr query (to filter results on the current store) - this may not be functionality that you want / require.
PlugIn.Search.PolicySet-1.0.0.json
In the section of type Sitecore.Commerce.Core.PolicySet at the top, in the Policies array, duplicate one of the objects and replace with your Entity name. eg:
{
  "$type": "Sitecore.Commerce.Plugin.Search.SearchViewPolicy, Sitecore.Commerce.Plugin.Search",
  "SearchScopeName": "MyObjectsScope",
  "ViewName": "MyObjectsDashboard"
},
I'm not sure if ^ this part is required (haven't tested without it), but it's probably good to have in case you add functionality to the business tools later.
Duplicate one of the 
SearchScopePolicy sections and rename the entities/lists so you have something like this:
{
  "$type": "Sitecore.Commerce.Plugin.Search.SearchScopePolicy, Sitecore.Commerce.Plugin.Search",
  "Name": "MyObjectsScope",
  "IncrementalListName": "MyObjectsIndex",
  "FullListName": "MyObjects",
  "DeletedListName": "DeletedMyObjectsIndex",
  "EntityTypeNames": {
    "$type": "System.Collections.Generic.List`1[[System.String, mscorlib]], mscorlib",
    "$values": [
    "Feature.MyFeature.Engine.Entities.MyObject"
    ]
  },
  "ResultDetailsTags": {
    "$type": "System.Collections.Generic.List`1[[Sitecore.Commerce.Core.Tag, Sitecore.Commerce.Core]], mscorlib",
    "$values": [{
      "$type": "Sitecore.Commerce.Core.Tag, Sitecore.Commerce.Core",
      "Name": "MyObjectsList"
    }]
  }
},
Duplicate one of the 
IndexablePolicy sections and rename the name and properties:
{
  "$type": "Sitecore.Commerce.Plugin.Search.IndexablePolicy, Sitecore.Commerce.Plugin.Search",
  "SearchScopeName": "MyObjectsScope",
  "Properties": {
    "EntityId": {
      "TypeName": "System.String",
      "IsKey": true,
      "IsSearchable": true,
      "IsFilterable": false,
      "IsSortable": false,
      "IsFacetable": false,
      "IsRetrievable": true
    },
    "ArtifactStoreId": {
      "TypeName": "System.String",
      "IsKey": false,
      "IsSearchable": false,
      "IsFilterable": true,
      "IsSortable": false,
      "IsFacetable": false,
      "IsRetrievable": false
    },
    "Name": {
      "TypeName": "System.String",
      "IsKey": false,
      "IsSearchable": true,
      "IsFilterable": false,
      "IsSortable": true,
      "IsFacetable": false,
      "IsRetrievable": true
    },
    "DisplayName": {
      "TypeName": "System.String",
      "IsKey": false,
      "IsSearchable": true,
      "IsFilterable": false,
      "IsSortable": true,
      "IsFacetable": false,
      "IsRetrievable": true
    },
    // ... etc. for rest of your fields
}
You will need to include 
ArtifactStoreId, as Sitecore will filter on this field automatically (with the ID of the current store) when generating the Solr query.  I haven't tested which fields are mandatory, but I think it's a good idea to index these 4 at a minimum.
Plugin.Habitat.CommerceMinions.json
In order to call the full / incremental index minions (or have them run automatically) to have your object indexed in Solr, you will need to create a couple of policies referencing your object. 
{
  "$type": "Sitecore.Commerce.Core.MinionPolicy, Sitecore.Commerce.Core",
  "ListToWatch": "MyObjects",
  "FullyQualifiedName": "Sitecore.Commerce.Plugin.Search.FullIndexMinion, Sitecore.Commerce.Plugin.Search",
  "ItemsPerBatch": 10
},
{
  "$type": "Sitecore.Commerce.Core.MinionPolicy, Sitecore.Commerce.Core",
  "WakeupInterval": "00:03:00",
  "ListToWatch": "MyObjectsIndex",
  "FullyQualifiedName": "Sitecore.Commerce.Plugin.Search.IncrementalIndexMinion, Sitecore.Commerce.Plugin.Search",
  "ItemsPerBatch": 10,
  "SleepBetweenBatches": 500
},
{
  "$type": "Sitecore.Commerce.Core.MinionPolicy, Sitecore.Commerce.Core",
  "WakeupInterval": "00:03:00",
  "ListToWatch": "DeletedMyObjectsIndex",
  "FullyQualifiedName": "Sitecore.Commerce.Plugin.Search.DeleteIndexDocumentsMinion, Sitecore.Commerce.Plugin.Search",
  "ItemsPerBatch": 10,
  "SleepBetweenBatches": 500
}
InitializeMyObjectsIndexingViewBlock.cs
Again we can base this off an existing class (eg. 
Sitecore.Commerce.Plugin.Orders.InitializeOrdersIndexingViewBlock).  This block is run during the index (full or incremental depending on what you put in 
ConfigureSitecore.cs below) and sets the values of the properties to be indexed.
public class InitializeMyObjectsIndexingViewBlock : PipelineBlock<EntityView, EntityView, CommercePipelineExecutionContext>
{
  public override Task<EntityView> Run(EntityView arg, CommercePipelineExecutionContext context)
  {
    Condition.Requires(arg).IsNotNull(string.Format("{0}: argument cannot be null.", Name));
    SearchIndexMinionArgument indexMinionArgument = context.CommerceContext.GetObjects<SearchIndexMinionArgument>().FirstOrDefault();
    if (string.IsNullOrEmpty(indexMinionArgument?.Policy?.Name))
      return Task.FromResult(arg);
    List<CommerceEntity> entities = indexMinionArgument.Entities;
    List<Entities.MyObject> source = entities != null ? entities.OfType<Entities.MyObject>().ToList() : null;
    if (source == null || !source.Any())
      return Task.FromResult(arg);
    KnownSearchViewsPolicy searchViewNames = context.GetPolicy<KnownSearchViewsPolicy>();
    source.ForEach(myObject =>
    {
      EntityView entityView = arg.ChildViews.Cast<EntityView>().FirstOrDefault(v =>
      {
        if (v.EntityId.Equals(myObject.Id, StringComparison.OrdinalIgnoreCase))
          return v.Name.Equals(searchViewNames.Document, StringComparison.OrdinalIgnoreCase);
        return false;
      });
      if (entityView == null)
      {
        entityView = new EntityView()
        {
          Name = context.GetPolicy<KnownSearchViewsPolicy>().Document,
          EntityId = myObject.Id
        };
        arg.ChildViews.Add(entityView);
      }
      entityView.Properties.Add(new ViewProperty()
      {
        Name = "EntityId",
        RawValue = myObject.Id
      });
      entityView.Properties.Add(new ViewProperty()
      {
        Name = "ArtifactStoreId",
        RawValue = context.CommerceContext.Environment.ArtifactStoreId
      });
      entityView.Properties.Add(new ViewProperty()
      {
        Name = "Name",
        RawValue = myObject.Name
      });
      entityView.Properties.Add(new ViewProperty()
      {
        Name = "DisplayName",
        RawValue = myObject.DisplayName
      });
   
      // ... etc. for rest of the fields
   
      }
    });
    return Task.FromResult(arg);
  }
}
You can also call other pipelines, or grab Components, (pretty much do whatever you like) to set property values.  You apparently 
cannot set values to 
null (unlike computed fields in Sitecore), you will have to use an empty string.
ConfigureSitecore.cs
From (again) taking a look at how the existing blocks are added, we can add ours: 
.ConfigurePipeline<IIncrementalIndexMinionPipeline>(c => c.Add<InitializeMyObjectsIndexingViewBlock>().After<InitializeIndexingViewBlock>())
.ConfigurePipeline<IFullIndexMinionPipeline>(c => c.Add<InitializeMyObjectsIndexingViewBlock>().After<InitializeIndexingViewBlock>())
// Also add this (see next section)
.ConfigurePipeline<IConfigureServiceApiPipeline>(configure => configure.Add<ConfigureServiceApiBlock>().After<Sitecore.Commerce.Plugin.Search.ConfigureServiceApiBlock>())
See the file below for an explanation for why we want to add our 
ConfigureServiceApiBlock after the one added by the Search plugin.
ConfigureServiceApiBlock.cs
What could we possibly need to add here? For some reason the existing implementation of the 
Search(...) call in the Engine (in 
Sitecore.Commerce.Plugin.Search.ConfigureServiceApiBlock) has omitted the "scope" parameter, so let's add it back in.  This is so that we can specify that we want to search our custom index (scope).
ActionConfiguration search = modelBuilder.Procedures.FirstOrDefault(p => p.Name == "Search") as ActionConfiguration;
if (search != null)
{
  search.Parameter("scope");
}
This code assumes the procedure has already been added by the Search plugin, which is why we need to patch our block after the Search block (the section above ^).  Note that this will add the "scope" parameter 
after the other parameters (ie. as the last parameter).  I'm sure you could add a bunch of extra code to swap the parameters around, but that is left as an exercise for the reader. 
Test the Engine index/search endpoints 
At this point you should be able to run the 
Run FullIndex Minion call in Postman (in the 
SitecoreCommerce_DevOps collection) with your scope name in the "WithListToWatch" body parameter.  After a few seconds you should see some entries in your Solr index.
You can then open the 
SearchApiSamples/API/Search call in Postman, change the name of the "scope" body parameter to the name of your index, and should see your indexed results towards the bottom of the response (search for "Name": "SearchResult" in the json response).
Sitecore
Sitecore.Commerce.ServiceProxy project
Make sure you update your 
CommerceShops endpoint, as it should now have the 
Search method with the 
scope parameter included!
MyObjectManager.cs 
(Or wherever you want to search from in your code)
You can use the following code to call the Search endpoint and return a list of results:
public MyObjectsResult SearchMyObjects(string shopName, string customerId, string term = "*", string filter = "", string orderBy = "", int top = 10, int skip = 0)
{
  var myObjectsResult = new MyObjectsResult();
  try
  {
    Sitecore.Commerce.Engine.Container container = EngineConnectUtility.GetShopsContainer(shopName: shopName, customerId: customerId);
    var result = Proxy.GetValue(container.Search(term, filter, orderBy, top.ToString(), skip.ToString(), MyObjectsScope));
    myObjectsResult.Success = true;
    if (result != null && result.Models.Count > 0)
    {
      EntityView ev = result.Models.First() as EntityView;
      if (ev != null && ev.ChildViews.Count > 0)
      {
        // ev.ChildViews is the list of results
        myObjectsResult.MyObjects = ev.ChildViews.Select(cv =>
        {
          EntityView myObj = cv as EntityView;
          return new Engine.Entities.MyObject
          {
            Id = myObj.GetPropertyValue("entityid"),
            Name = myObj.GetPropertyValue("name"),
            DisplayName = myObj.GetPropertyValue("displayname"),
            // ... etc.
          };
        });
      }
    }
  }
  catch (Exception ex)
  {
    Log.Error($"Unable to search myobjects using term:'{term}', filter:'{filter}', orderBy:'{orderBy}', top:'{top}', skip:'{skip}'", ex, this);
  }
  return myObjectsResult;
}
Which is referencing an extension method I've created, to grab a property from the EntityView
public static string GetPropertyValue(this EntityView ev, string property)
{
  return ev.Properties.FirstOrDefault(p => p.Name == property)?.Value;
}
Test it out!
That's all there is to it! If you could get results from your Postman call in the Engine section above, you should now get the same results in Sitecore.
Hopefully this comes in handy for some of you out there doing Commerce work.  Let me know if you come across any issues or better ways of going about searching a Commerce index.
Big thanks to 
Andrew Sutherland (knower of all things Commerce) for his Commerce help.  Check out 
his blog for lots of great Commerce posts.