If you have 2 large chicken breasts cut them in half to get 4 thinner chicken cutlets. Pound the chicken to make it an even ½-inch thickness if needed. Season the chicken generously on both sides with salt and pepper.

Heat 1 tablespoon of oil in a large, oven-proof skillet over medium-high heat. Brown the chicken, about 2 minutes per side. Once browned, remove to a plate. (The chicken will not fully cooked yet.)

Add the remaining tablespoon of olive oil to the pan. Add the sliced onions and cook on medium-low, stirring and scrapping up the brown bit on the bottom every few minutes. Continue to cook until the onions are well caramelized and a deep brown color, about 20 minutes.

Stir in the garlic and thyme then season with the teaspoon of salt and ¼ teaspoon of pepper. Cook for an additional minute to soften the garlic.

Add the balsamic vinegar and stir, scrapping up any brown bits stuck to the bottom of the pan.

Stir in the broth and Worcestershire sauce. Add the chicken back to the pan with any juices that have collected on the plate and simmer on medium-low for 6 minutes, for until the chicken is fully cooked and has an internal temp of 165F, flipping the chicken over halfway through.

Preheat the broiler. Once the chicken is fully cooked, spoon some of the onion mixture over the chicken then sprinkle with the shredded cheese. Broil until the cheese is bubbly. (Alternatively, you can just cover the pan for a minute to let the cheese melt.) Serve right away with some extra thyme leaves on top for garnish.