Combine flour with salt and pepper in a shallow dish.Dredge chicken cutlets in seasoned flour.Cutlets should be approximately 4 ounces each.
Cook in 2 TB. melted butter, and a little olive oil if needed, over medium heat in large skillet until done, turning often.Set chicken aside, cover and keep warm.Make sauce.
Melt 2 TB butter in the same skillet.Add mushrooms and onion, cook until tender, about 3 minutes.
Sprinkle 1 TB of the seasoned flour over mushroom mixture, stir and cook 1 minute.
Add wine, cook and stir 1 minute.
Add broth and thyme.Bring to a boil, stir 2 minutes, until sauce is thickened.