How to connect a Load balancer and an Interface VPC Endpoint together using CDK?

You'll need to use a Custom Resource to (call the API to) get the IP of the endpoint's network interface(s) as CloudFormation doesn't expose it as a return value, which means CDK can't offer it as a property.

(Note: this code was originally written for CDK ~1.40, but should still work or be easily updatable.)

Assuming you're creating the VPC Endpoint like this:

    // note: creates two endpoints because this VPC has two private subnets
    const VPCEndpoints = new ec2.InterfaceVpcEndpoint(this, "APIEndpoint", {
      vpc: my_vpc,
      service: ec2.InterfaceVpcEndpointAwsService.APIGATEWAY,
      subnets: { subnetType: ec2.SubnetType.PRIVATE },
    });

Then you can create a custom resource to call the DescribeNetworkEndpoints API on them. This will be a Lambda function which CloudFormation will deploy and then invoke, and the return value from the function will have the API response in.

CDK has a helper which makes it easy to deploy a custom resource that just calls an AWS API, so we can use that. (CDK writes a little nodeJS function for us to do it, which is why I've linked to the JS SDK above.)

    const eni = new custom_resources.AwsCustomResource(
      this,
      "DescribeNetworkInterfaces",
      {
        onCreate: {
          service: "EC2",
          action: "describeNetworkInterfaces",
          parameters: {
            NetworkInterfaceIds: VPCEndpoints.vpcEndpointNetworkInterfaceIds,
          },
          physicalResourceId: PhysicalResourceId.of(Date.now().toString()),
        },
        onUpdate: {
          service: "EC2",
          action: "describeNetworkInterfaces",
          parameters: {
            NetworkInterfaceIds: VPCEndpoints.vpcEndpointNetworkInterfaceIds,
          },
          physicalResourceId: PhysicalResourceId.of(Date.now().toString()),
        },
        policy: {
          statements: [
            new iam.PolicyStatement({
              actions: ["ec2:DescribeNetworkInterfaces"],
              resources: ["*"],
            }),
          ],
        },
      }
    );

We can now use the getResponseField() method on the eni object to read the response values from the API call, and then use them to create an ALB Target Group.

    // note: two ENIs in our endpoint as above, so we can get two IPs out of the response
    const ip1 = eni.getResponseField("NetworkInterfaces.0.PrivateIpAddress");
    const ip2 = eni.getResponseField("NetworkInterfaces.1.PrivateIpAddress");

    const ALBTargetGroup = new elbv2.ApplicationTargetGroup(this, "ALBTG", {
      port: 443,
      targetType: elbv2.TargetType.IP,
      vpc: my_vpc,
    });

    ALBTargetGroup.addTarget(new elbv2_targets.IpTarget(ip1));
    ALBTargetGroup.addTarget(new elbv2_targets.IpTarget(ip2));

The target group can then just be used in an ALB Listener as usual.