Sauté mushrooms over medium heat for 3-5 minutes in a cast iron skillet with 2 tablespoons of butter. I also used a splash of olive oil and a pinch of garlic salt and pepper. Set aside.
Using the flat side of a meat mallet, tenderize the chicken and flatten it out to approximately 1/4 inch thick.
Dredge chicken in flour and cook in a cast iron skillet on both sides until cooked through and skin is starting to turn brown and crispy. Add a pinch of garlic salt and pepper. Set aside.
Using the same skillet you cooked the chicken in, add the juices from the mushrooms, the remaining butter, wine, chicken broth, red wine vinegar, chicken bouillon, and the mixture of corn starch and water. Stir until combined and bubbling. This will create a rich gravy like broth to pour over the chicken. Add more water if it gets to thick.
In a 9 x 13 inch baking dish, layer the chicken, mushrooms, cheeses, and green onions (slice approximately 3 green onions) and bake at 450 degrees for 15-20 minutes. My oven worked best at 22 minutes.
I did not measure the cheeses perfectly but they came out to be around 2 cups of mozzarella cheese and 2 cups of Parmesan cheese.
Serve hot with a side.