In a large skillet, melt the butter over medium heat. Add the sliced onions and cook, stirring occasionally, until they are caramelized and golden brown, about 15 minutes.
Add the minced garlic and cook for an additional 1-2 minutes until fragrant.
Push the onions to the side of the skillet and add the chicken breasts to the center. Season with salt and pepper.
Cook the chicken for about 5 minutes on each side until browned.
Pour the beef broth over the chicken and add the thyme and Worcestershire sauce. Bring to a simmer and cover the skillet.
Reduce the heat to medium-low and let it cook for an additional 15 minutes, or until the chicken is cooked through (internal temperature of 165°F).
Once the chicken is cooked, remove the lid and place the caramelized onions on top of each chicken breast, then sprinkle with shredded Swiss cheese.
Place the skillet under the broiler for 2-3 minutes, or until the cheese is melted and bubbly.
Remove from the oven and garnish with fresh parsley before serving.