Peel eggplant if desired; cut in ½″ slices. Sprinkle with salt. Dip in egg and then in crumbs. Dry on rack a few minutes.
Pour oil into skillet to the depth of ⅛″ and heat. Brown eggplant slices on both sides in hot oil. Place slices in a shallow baking pan, overlapping if necessary. Sprinkle with pepper, parsley and Parmesan cheese; top with mozzarella cheese sl