Peel the eggplants and cut them in slices about 3/8 inch thick. Set the slices in a pasta colander and sprinkle with salt. Put a soup dish under the colander to collect the drippings and let stand until drained. Add enough oil to a large skillet to come 1 inch up the side of the pan. Dip slices in beaten egg and coat with bread crumbs. Take as many slices as you think will fit in one layer in the skillet. Fry to a golden brown on both sides, then transfer to a platter lined with paper towels to drain. Line the bottom of a bake and serve dish with a single layer of fried eggplant slices. Top the layer with tomato sauce, sprinkle with Parmesan cheese and mozzarella cheese. Cover with another layer of eggplant. Continue building up layers of eggplant, tomato sauce, and cheeses until you have used all the eggplant. You can also use a pound of ricotta in between the layers. Preheat oven to 350 degrees and bake for approximately 1 hour.