Preheat oven to 350F. Place an oven-proof bowl or baking dish full of water on the bottom rack.
Prepare the egg dipping sauce and the breadcrumbs mixture: In one container, combine the egg, milk, salt, pepper, and a few dashes of hot sauce. Mix well. In another container, combine the Italian breadcrumbs and the crumbled Parmesan cheese. Mix well.
Bread the chicken: Dip each chicken breast into the egg mixture, and then press firmly into the breadcrumbs on both sides. Then repeat - dip each chicken into the egg mixture again, and press into the breadcrumbs on both sides to get a nice even coating.
Heat the olive oil in a large skillet. Carefully place the chicken breasts into the skillet, smooth side down. Cook for 2-3 minutes on each side, or until golden brown.
Add 1 cup of marinara sauce to a 13 x 9 casserole pan (or similar size). Carefully place the chicken breasts into the casserole pan. Spoon a quarter cup of marinara sauce sauce on top of each chicken breast and place in the oven to bake at 350, until the chicken is almost cooked. Cooking time will vary depending on the chicken breast size, anywhere from 15 to 30 minutes. Cook until a thermometer inserted into the thickest part of the chicken breast registers 155-160F.
Spoon more sauce on each chicken breast if you like things extra saucy, and top each one with a slice of mozzarella and a bit of Parmesan cheese. Bake for another 7-10 minutes, until the cheese is melted and bubbly, and the chicken is fully cooked to 165F.To serve, spoon some sauce onto a plate, and place the chicken on top of the sauce.
If you don't have Italian breadcrumbs, use regular breadcrumbs and add a bit of salt and some dried herbs, such as oregano, basil, parsley, marjoram, or any combination of these herbs.