How to create a task (TPL) running a STA thread?

You can use the TaskScheduler.FromCurrentSynchronizationContext Method to get a TaskScheduler for the current synchronization context (which is the WPF dispatcher when you're running a WPF application).

Then use the ContinueWith overload that accepts a TaskScheduler:

var scheduler = TaskScheduler.FromCurrentSynchronizationContext();

Task.Factory.StartNew(...)
            .ContinueWith(r => AddControlsToGrid(r.Result), scheduler);