Pat the chicken cutlets completely dry with paper towels. Season both sides evenly with kosher salt, black pepper, and garlic powder.

Heat 1 tablespoon of olive oil and 1 tablespoon of butter in a large 12-inch oven-safe skillet (such as cast iron) over medium-high heat. Add the chicken cutlets and sear for 3 to 4 minutes per side until deeply golden brown. Transfer chicken to a clean plate (it will finish cooking in the sauce).

Reduce heat to medium. Add the remaining 1 tablespoon of olive oil and 1 tablespoon of butter to the same skillet. Add the sliced onions and a pinch of salt. Cook, stirring occasionally, for 12 to 15 minutes until the onions turn golden brown, tender, and intensely sweet.

Stir in the minced garlic and cook for 1 minute until fragrant. Sprinkle the flour over the onions and stir continuously for 1 minute to cook out the raw flour flavor.

Slowly pour in the beef broth while deglazing the bottom of the skillet with a wooden spoon, scraping up all flavorful browned bits. Stir in the Worcestershire sauce, Dijon mustard, fresh thyme, and bay leaf. Bring to a gentle simmer for 3 minutes until the gravy thickens slightly.

Nestle the seared chicken cutlets back into the bubbling onion gravy. Spoon some of the caramelized onions over each chicken piece. Top generously with shredded Gruyère and Swiss cheese.

Transfer the skillet to an oven preheated to 400°F (200°C) or switch on the broiler for 3 to 4 minutes until the cheese is completely melted, bubbling, and golden brown with toasted spots.

Remove carefully using heat-proof mitts. Discard the bay leaf, garnish with fresh thyme leaves, and let rest for 3 minutes before serving warm directly from the skillet.