Consider Using async without await.
think that maybe you misunderstand what async does. The warning is exactly right: if you mark your method async
If Logger.LogInfo is a synchronous method, the whole call will be synchronous anyway. If all you want to do is to execute the code in a separate thread, async is not the tool for the job. Try with thread pool instead:
ThreadPool.QueueUserWorkItem( foo => PushCallAsync(callNotificationInfo) );