Preheat your oven to 375°F (190°C).
In a large skillet, heat the olive oil over medium heat. Add the sliced onions and cook, stirring occasionally, for about 15-20 minutes until they are caramelized and golden brown.
Season the chicken breasts with salt, pepper, garlic powder, and thyme. Place them in a baking dish.
Pour the beef broth over the chicken breasts. Top each chicken breast with the caramelized onions, then sprinkle the Swiss cheese and Parmesan cheese evenly over the top.
Cover the baking dish with aluminum foil and bake in the preheated oven for 25 minutes.
Remove the foil and bake for an additional 15-20 minutes, or until the chicken is cooked through and the cheese is bubbly and golden.
Let the dish rest for 5 minutes before serving. Garnish with fresh parsley.