Season & sear chicken: Season chicken cutlets on both sides with kosher salt, cracked black pepper, and garlic powder. Heat 1 tbsp olive oil and 1 tbsp butter in a large oven-safe cast iron skillet over medium-high heat. Sear chicken 4-5 minutes per side until golden brown and cooked through (165°F / 74°C). Transfer to a plate.

Caramelize the onions: In the same skillet, melt remaining butter and oil over medium heat. Add sliced onions and 1/2 tsp salt. Cook, stirring occasionally, for 15-18 minutes until deeply golden, tender, and caramelized. Add minced garlic and cook 1 minute.

Build the pan gravy: Sprinkle 1 tablespoon flour over the onions and stir for 1 minute. Slowly pour in beef bone broth and Worcestershire sauce, scraping up any delicious browned fond bits from the skillet floor. Add fresh thyme leaves and simmer 3-4 minutes until gravy is rich, glossy, and slightly thickened.

Assemble & melt cheese: Return seared chicken breasts to the skillet, spooning generous heaps of caramelized onions and rich gravy over each breast. Blanket tops evenly with shredded Gruyère and mozzarella cheese.

Broil & serve: Transfer skillet under the oven broiler on HIGH for 2 to 3 minutes until cheese is bubbly, melted, and flecked with golden-brown spots. Garnish with fresh thyme sprigs and serve piping hot.