Slice the eggplant and set aside. Find a bowl in which the eggplant rounds can lie flat and lightly beat the egg whites and salt, if using,in it. In another large bowl, combine the bread crumbs, Parmesan cheese, garlic, and basil.
Dip the eggplant slices in the egg whites, then dredge them in the bread crumb mixture to coat both sides evenly. Place the breaded slices on a baking sheet that has been prepared with a light coating of oil. Bake the eggplant for about 20 minutes on each side, until tender and easily pierced with a fork.
Spread about half of the sauce in the bottom of an 8 X 12-inch glass or nonreactive baking dish. Layer about half of the eggplant slices on top of the sauce. Spread all of the ricotta cheese evenly on the eggplant and top with about l 1/2 cups of the mozzarella. Use the rest of the eggplant slices for a second layer. Cover them with the remaining sauce and any extra bread crumb mixture. Sprinkle the top with the final 1/2 cup of mozzarella and bake, uncovered, for 25 to 30 minutes, until the cheese is melted and bubbly.