Make the bread coating: In a shallow bowl, whisk together 1 egg and 2 tablespoons of milk until well combined. In another bowl, mix ½ cup breadcrumbs with ¼ cup grated Parmesan and 2 tablespoons chopped Italian parsley.
Prepare the chicken: Pound 2–3 boneless, skinless chicken breasts until thin and even. Season both sides with salt and pepper. Dip each piece first in the egg mixture, then coat thoroughly in the breadcrumb mixture.
Pan-fry the chicken: Heat oil in a large skillet over medium-high heat. Fry the chicken in batches for 2–3 minutes per side, or until golden brown. Transfer to a paper towel-lined plate to drain.
Assemble the dish: Preheat oven to 375°F (190°C). Spread 1 cup of marinara sauce on the bottom of a 9×13-inch casserole dish. Place the fried chicken on top. Cover with another cup of marinara and sprinkle with the remaining ¼ cup of Parmesan.
Bake: Cover with foil and bake for 20 minutes. Remove the foil, top with 1 cup of shredded mozzarella, and bake uncovered for another 10 minutes, or until the cheese is bubbly and golden.
Finish and serve: Sprinkle with more Parmesan and fresh parsley if desired. Serve hot.