Prepare and Season the Chicken: Place each chicken breast on a cutting board and slice horizontally to create two thinner cutlets. If needed, gently pound with a meat mallet or rolling pin until each piece is about ¾ inch thick. Sprinkle both sides with half of the salt and all the black pepper to enhance the flavor before cooking.
Coat in Flour and Sear: Add the flour to a shallow dish. Dredge each chicken cutlet, coating both sides lightly, and shake off the excess. Heat olive oil in a 12-inch oven-safe skillet over medium-high heat. Sear the chicken for about 3 minutes per side until lightly golden but not fully cooked through. Transfer to a plate and set aside.
Caramelize the Onions: In the same skillet, melt the butter over medium heat. Add sliced onions and the remaining salt. Cook, stirring frequently, for about 20 minutes total, allowing the onions to soften first, then slowly develop a rich, golden-brown color. If the bottom of the pan darkens too much, splash in a tablespoon of broth or water and scrape up the browned bits for extra flavor.
Build the Flavor Base: Stir in the minced garlic and cook for 1–2 minutes until fragrant. Sprinkle the reserved flour (about 2 tablespoons from dredging) over the onions, stirring well to coat. Cook for another 2 minutes to eliminate the raw flour taste.
Create the Sauce: Pour in the beef broth and Worcestershire sauce, followed by the chopped thyme. Stir continuously, scraping up all the caramelized bits from the skillet’s surface. Simmer for 2–3 minutes until the sauce slightly thickens.
Assemble and Bake: Nestle the seared chicken cutlets into the onion mixture. Spoon some of the caramelized onions over each piece, then generously top with shredded Gruyere cheese. Transfer the skillet to a preheated oven at 400°F (200°C) and bake for 6–8 minutes until the chicken is fully cooked and the cheese is melted and bubbling.
Garnish and Serve: Remove from the oven and let rest for a minute. Sprinkle with fresh thyme leaves and cracked black pepper. Serve immediately with crusty bread, mashed potatoes, or a simple side salad to soak up the flavorful onion gravy.