Caramelize onions: Heat butter and 1 tablespoon olive oil in a large oven safe skillet over medium heat. Add in onions and cook for 10-15 minutes stirring every 5 minutes or so. If the onions are getting too brown turn down the heat to medium low. Add in the marsala and scrape the bottom of the pan to remove any fond aka "brown bits". This adds so much flavor! Remove the onions from the pan and set aside on a plate.
Season chicken: On both sides with italian seasoning, salt and pepper.
Cook chicken: Add 1 tablespoon olive oil to the same pan the onions were cooked in. Heat oil over medium high heat and when the oil starts to sizzle add in chicken breasts. Cook chicken for 4-5 minutes on each side until golden brown. Remove from the pan and set aside on a plate.
Make the sauce: Return the onions back to the pan and stir in flour. Cook for one minute stirring constantly so it doesn't burn. Slowly whisk in the beef broth and bring the mixture to a simmer. Simmer for 2-3 minutes or until the mixture is thickened.
Melt cheese: Preheat oven broiler to high. Add the chicken back to the pan and top each chicken breast with a slice of swiss and a slice of provolone cheese. Place in the oven and broil until cheese is melted and bubbly.
Serve immediately: with fresh chopped parsley for garnish, if desired.