Is it possible

Blocking.cs

public class BackgroundQueuedHostedService : BackgroundService
{
    protected override async Task ExecuteAsync(CancellationToken cancellationToken)
    {
           while (!cancellationToken.IsCancellationRequested)
           {
               var workItem = await TaskQueue.DequeueAsync(cancellationToken);
               await FastTask(); // 
               await Task.Factory.StartNew(
                                () => 
                                {
                                    // Blocking call
                                },
                                CancellationToken.None,
                                TaskCreationOptions.LongRunning & TaskCreationOptions.DenyChildAttach,
                                TaskScheduler.Default);
           }
    }
}