Combine the eggs, water, salt, and pepper to taste in a mixing bowl. Combine the crumbs and cheese in a shallow plate.
Cut the unpeeled eggplant into thin slices, about one-eighthinch thick. Dip them into the egg mixture, then into the cheese-crumb mixture, coating as thoroughly as possible.
Pour the oil into a skillet to the depth of one-quarter inch. Heat the oil. Cook the eggplant, a few slices at a time, on both sides until golden brown. Add more oil when necessary to keep slices from sticking. Drain on paper towels.