Preheat oven to 450 and grease a 9x13 baking dish with nonstick cooking spray. Set aside.
For large chicken breasts, slice in half lengthwise. Place the chicken between two pieces of plastic wrap and use a meat tenderizer to flatten to 1/4 inch thickness. Season both sides with salt and pepper.
Slice mushrooms into thin slices.
Place flour into a shallow dish and coat both sides of the chicken in flour. Reserve remaining flour.
Add 2 tablespoons butter to a skillet and heat over medium heat. Working in batches, (and adding 1 tablespoon butter to each new batch) brown chicken on both sides, about 3 minutes each side.
Remove from pan and place into prepared baking dish. Chicken can overlap.
In the same skillet, add 2 tablespoons butter and mushrooms. Heat over medium heat, stirring occasionally until mushrooms are tender, about 3 minutes.
Add Mushrooms on top of chicken.
In the same skillet, add Marsala, chicken broth and season with salt. Heat over medium high and continue to boil until reduced to about half, or 8 minutes.
Drizzle sauce on top of chicken and mushrooms.
Mix together the cheese and sprinkle on top of the chicken. Bake for 6-7 minutes or until cheese is melted.
With remaining mixture in the skillet, add 2 tablespoons reserved flour and remaining butter. Heat over medium heat, whisking constantly until thick and hot. Serve chicken with sauce on the side.