pseudocode.cs

private void action()
{
    ...
        
    // some very long process here which blocks the code execution
    ...
        
    var context = GlobalHost.ConnectionManager.GetHubContext<SomeHub>();
    context.Clients.All.FileReady("sample.txt");
}

...
// web-api controller
public class SomeController : ApiController
{
    [Route("sample")]
    [HttpPost]
    public string Sample([FromBody] dynamic data)
    {
        ...
        
        new Task(action).Start(); // works fine
        
        // doesn't work
        //Task.Run(() => action());
        //Task.Factory.StartNew(action, CancellationToken.None, TaskCreationOptions.None, TaskScheduler.Current);
        //Task.Factory.StartNew(action, CancellationToken.None, TaskCreationOptions.LongRunning, TaskScheduler.Default);
        
        return "ok";
    }
}