Heat butter and oil in a skillet.
Add sliced onions and cook slowly.
Stir often until onions turn golden.
Add thyme, salt, and pepper.
Sprinkle flour and stir for coating.
Pour in both broths and simmer.
Remove onions once thickened.
Season chicken with garlic powder.
In the same pan, sear chicken.
Brown both sides, then reduce heat.
Place chicken in oven-safe dish.
Cover chicken with caramelized onions.
Sprinkle both cheeses generously on top.
Bake until chicken is fully cooked.
Serve hot and enjoy the dish.