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 them slowly, stirring frequently, for about 15 minutes until they are caramelized and golden brown.
Add minced garlic to the skillet and cook for another minute until fragrant. Remove from heat and set aside.
In a casserole dish, season the chicken breasts with salt, black pepper, and thyme. Pour the beef broth and heavy cream over the chicken.
Spread the caramelized onion and garlic mixture evenly over the chicken.
Sprinkle the shredded Swiss cheese on top of the casserole.
Cover the dish with aluminum foil and bake in the preheated oven for 25 minutes.
Remove the foil and sprinkle the French fried onions over the cheese. Bake uncovered for an additional 15 minutes, or until the cheese is melted and bubbly.
Once done, let it rest for a few minutes before serving. Garnish with fresh parsley if desired.