Beat together egg, egg whites, and water in a shallow bowl. Dip eggplant slices in egg, then bread crumbs. Place in a single layer on a baking sheet. Bake in preheated oven until fork tender, 7 to 10 minutes on each side.
Spread spaghetti sauce to cover the bottom of a 9x13-inch baking dish. Place a layer of eggplant slices in the sauce. Sprinkle with mozzarella and Parmesan cheeses. Repeat with remaining ingredients, ending with cheeses. Sprinkle basil on top.
Bake in preheated oven until golden brown, about 35 minutes.