Preheat oven to 350F.
Combine the flour, parmesan, salt and pepper in a shallow bowl or plate with a rim.
Place chicken breasts in a gallon sized Ziploc bag. Using a meat mallet, pound meat on both sides until it is flattened to 1/4 to 1/2 of an inch. (Some are easier to flatten than others. If they are really thick, I will cut them in half through the middle into to thinner breasts).
Coat each piece of chicken egg white, then dip both sides into the in parmesan mixture. In a cast iron skillet, heat 1 tablespoon of oil over medium-high heat. Add chicken pieces to the pan, cooking cook 5 minutes per side - or until golden.
Add chicken to a lightly greased 9x13 pan. Pour a large spoonful of sauce on top of each breast, then top with mozzarella. Bake at 350F for 5-10 minutes (or until chicken is cooked through and cheese is melted.
Serve with pasta and additional sauce.