Combine the bread crumbs and oil in a 12-inch skillet and toast over medium heat, stirring often, until golden, about 10 minutes. Spread the bread crumbs in a shallow dish and cool slightly; when cool, stir in the Parmesan.
In a second shallow dish, combine the flour, garlic powder, 1 tablespoon salt, and ½ teaspoon pepper together. In a third shallow dish, whisk the egg whites and water together.
Line a rimmed baking sheet with foil, place a wire rack on top, and spray the rack with vegetable oil spray. Pat the chicken dry with paper towels, then season with salt and pepper.
Lightly dredge the cutlets in the flour, shaking off the excess, then dip into the egg whites, and finally coat with the bread crumbs, Press on the bread crumbs to make sure they adhere. Lay the chicken on the wire rack.
Spray the tops of the chicken with vegetable oil spray. Bake until the meat is no longer pink in the center and feels firm when pressed with a finger, about 15 minutes, flipping to the other side after 10 minutes.
Remove the chicken from the oven. Spoon 2 tablespoons of the sauce onto the center of each cutlet and top the sauce with 2 tablespoons of the mozzarella. Return the chicken to the oven and continue to bake until the cheese has melted, about 5 minutes.