Preheat your oven to 400 degrees F.
Place an oven-safe skillet over medium-high heat and add the butter, melting it until bubbly.
Add the sliced onions to the skillet and stir. Cook for about 20 to 30 minutes until translucent and softened.
Sprinkle the chicken breasts with olive oil, salt, pepper, dried basil, and dried Italian herbs. Ensure they are evenly coated.
Once the onions are done, remove them from the skillet and set aside.
Place the chicken breasts in the pan and cook for 5 to 6 minutes per side until nicely browned. Cover with foil to keep warm.
Return the onions to the skillet and sprinkle with cornstarch. Stir in the beef broth and Worcestershire sauce, whisking until the cornstarch is dissolved.
Once thickened, add the chicken back to the skillet and spoon sauce over the chicken.
Top each chicken breast with a slice of provolone cheese and a slice of Swiss cheese.
Transfer the skillet to the oven and cook for 8 to 10 minutes until the cheese is melted and browned.
Spoon the sauce and onions over the chicken and garnish with parsley.