Preheat your oven to 350°F (175°C).
In a large skillet, heat the olive oil over medium heat. Add the sliced onions and sprinkle with salt. Cook, stirring occasionally, until the onions are golden brown and caramelized, about 15-20 minutes.
While the onions are cooking, season the chicken breasts with black pepper, garlic powder, and dried thyme.
In a separate pan, sear the seasoned chicken breasts over medium-high heat for about 3-4 minutes on each side, until they are browned. Remove from heat and set aside.
In a bowl, combine the beef broth and sour cream, mixing until well combined.
In your casserole dish, layer the caramelized onions on the bottom, followed by the seared chicken breasts. Pour the beef broth and sour cream mixture over the chicken, ensuring it is well covered.
Sprinkle the cubed French bread evenly across the top of the casserole and then add the shredded Gruyère cheese.
Cover the casserole dish with aluminum foil and bake in the preheated oven for 25 minutes.
Remove the foil and bake for an additional 15 minutes, or until the cheese is bubbly and golden brown.
Remove from the oven and let it cool for a few minutes. Garnish with chopped parsley before serving.