[ContentType(GUID = "F40176A2-E3A2-43F8-A18B-2A133D5D8BBC", DisplayName = "Test Page")]
public class TestPage : PageData
{
    [AllowedTypes(typeof(TestBlock))]
    [Display(Name = "Child", Order = 10)]
    public virtual ContentReference Child { get; set; }
}

[ContentType(GUID = "9DDFEF96-AB5B-42CD-80D0-31D9E65ADAE6", DisplayName = "Test Block")]
public class TestBlock : BlockData
{
    [Display(Order = 5)]
    public virtual string Heading { get; set; }


    [Display(Name = "Child", Order = 10)]
    [AllowedTypes(typeof(TestBlock))]
    public virtual ContentReference Child { get; set; }
}

This is an example response when calling the content delivery API with an expand property set to '*'.  See that the first block from the page is expanded but the second is not (i've commented the JSON).

{
  "contentLink": {
    "id": 202,
    "workId": 0,
    "guidValue": "5ff3fc26-7a31-4820-b947-2a918e222065",
    "providerName": null,
    "url": "/test/",
    "expanded": null
  },
  "name": "Test",
  "language": {
    "link": "/test/",
    "displayName": "English",
    "name": "en"
  },
  "existingLanguages": [
    {
      "link": "/test/",
      "displayName": "English",
      "name": "en"
    }
  ],
  "masterLanguage": {
    "link": "/test/",
    "displayName": "English",
    "name": "en"
  },
  "contentType": [
    "Page",
    "TestPage"
  ],
  "parentLink": {
    "id": 5,
    "workId": 0,
    "guidValue": "1611ac34-e475-41fe-b278-1be758763003",
    "providerName": null,
    "url": "/",
    "expanded": null
  },
  "routeSegment": "test",
  "url": "/test/",
  "changed": "2022-02-25T12:02:15Z",
  "created": "2022-02-25T12:02:06Z",
  "startPublish": "2022-02-25T12:02:15Z",
  "stopPublish": null,
  "saved": "2022-02-25T12:04:54Z",
  "status": "Published",
  "category": [],
  "requiresAuthentication": null,
  "meta": {
    "title": "",
    "description": "",
    "robots": ""
  },
  "child": { // this is the first block referenced by the page
    "id": 204,
    "workId": 0,
    "guidValue": "ca5cae7a-06af-420d-806d-0c9a49e36b43",
    "providerName": null,
    "url": null,
    "expanded": {
      "contentLink": {
        "id": 204,
        "workId": 0,
        "guidValue": "ca5cae7a-06af-420d-806d-0c9a49e36b43",
        "providerName": null,
        "url": null,
        "expanded": null
      },
      "name": "Test 1",
      "language": {
        "link": null,
        "displayName": "English",
        "name": "en"
      },
      "existingLanguages": [
        {
          "link": null,
          "displayName": "English",
          "name": "en"
        }
      ],
      "masterLanguage": {
        "link": null,
        "displayName": "English",
        "name": "en"
      },
      "contentType": [
        "Block",
        "TestBlock"
      ],
      "parentLink": {
        "id": 203,
        "workId": 0,
        "guidValue": "0fd61ab0-e440-4084-88ab-4eeefcd35c66",
        "providerName": null,
        "url": "/contentassets/0fd61ab0e440408488ab4eeefcd35c66/",
        "expanded": null
      },
      "routeSegment": null,
      "url": null,
      "changed": "2022-02-25T12:02:59Z",
      "created": "2022-02-25T12:02:37Z",
      "startPublish": "2022-02-25T12:02:59Z",
      "stopPublish": null,
      "saved": "2022-02-25T12:05:07Z",
      "status": "Published",
      "category": [],
      "heading": "Test 1",
      "child": { // here is the child property of the block which should be another block with a heading etc. but 'expanded' is null?
        "id": 206,
        "workId": 0,
        "guidValue": "5f05d107-8973-46c6-9e37-3c71729d283a",
        "providerName": null,
        "url": null,
        "expanded": null
      }
    }
  }
}