Preheat oven to 375°F. In a shallow dish, combine flour with 1/2 tsp. salt and 1/4 tsp. pepper. In a bowl, beat together eggs and 2 Tbsp. water. Place bread crumbs in another shallow dish.
Dredge chicken in flour, shaking off excess. Dip into egg mixture, letting excess drain. Dredge in bread crumbs, pressing on gently. Place on wax paper-lined baking sheet.
In a large skillet, heat 2 Tbsp. oil over mediumhigh heat. Add one-quarter of cutlets. Cook until golden, 1 1/2 to 2 minutes per side. Transfer to a paper towel- lined baking sheet. Continue cooking with oil and chicken in three more batches.
Pour half of spaghetti sauce into a 13-inch baking pan. Place one layer of cutlets on top. Cover with half of mozzarella and half of Parmesan. Layer with other cutlets and sauce. Sprinkle with remaining mozzarella and Parmesan. Bake until hot and bubbling, 20 minutes.