Preheat Oven:
Set oven to 375°F (190°C). Lightly grease a 9x13-inch baking dish.
Caramelize the Onions:
In a large skillet, heat olive oil and butter over medium heat. Add the sliced onions, sugar, salt, pepper, and thyme. Cook slowly, stirring often, for 20–25 minutes until golden brown and deeply caramelized.
Deglaze & Finish Onions:
Pour in the broth and stir, scraping up any browned bits. Simmer for another 2–3 minutes until slightly reduced. Set aside.
Prepare Chicken:
Arrange the chicken breasts in the baking dish. Season lightly with salt and pepper. Spoon the caramelized onions and broth mixture over the top.
Add Cheese & Bake:
Sprinkle mozzarella and Gruyère evenly over the chicken and onions. Bake uncovered for 25–30 minutes, or until chicken reaches 165°F internally and cheese is bubbly and golden.
Serve:
Let rest for 5 minutes before serving. Garnish with chopped parsley if desired. Delicious with mashed potatoes, rice, or crusty bread.