Place the chicken breasts on a cutting board in between two sheets of plastic wrap. Using a mallet, pound chicken thin. Season both sides with salt and pepper.
Combine bread crumbs and cheese in a shallow bowl. Dip the chicken in the beaten egg, then dredge in the bread crumb mixture, turning to coat both sides.
Heat olive oil in a large, non-stick skillet over medium heat. Place the chicken in the skillet (you might have to batches or use two skillets) and cook until golden, 3 minutes per side. Spread the marinara sauce onto the bottom of an 8x8 baking dish. Preheat the broiler.
Transfer the chicken pieces to the baking dish, placing them on top of the sauce. Top each chicken piece with slices of fresh mozzarella. Broil about 4 inches from the heat until the sauce is hot, cheese is melted and chicken is cooked through, about 5-8 minutes. Garnish with parsley and serve.