Preheat oven to 400°F (200°C).

Melt butter and olive oil in a large skillet over medium heat. Add the sliced onions and cook slowly for 20-25 minutes, stirring occasionally, until they are deep golden brown and caramelized.

Stir in the beef broth and fresh thyme, scraping up any browned bits from the bottom of the pan. Simmer for 2 minutes, then remove the onions to a bowl.

Season the chicken breasts with salt, pepper, and garlic powder. In the same skillet, sear the chicken for 3-4 minutes per side until browned.

Transfer the chicken to a baking dish. Pile the caramelized onions generously on top of each chicken breast.

Place a slice of Gruyère cheese over the onions on each breast.

Bake for 15 minutes, or until the chicken is cooked through (165°F) and the cheese is melted, bubbly, and slightly browned.