Peel the eggplant and cut it into paper -thin slices.
Layer the slices in a colander, lightly salting each layer and sit a plate on top, touching the eggplant. Put a heavy can on top of the plate and let the eggplant drain for about an hour, then rinse off the salt and pat the slices dry.
Preheat the over to 400°F.
Beat the eggs in a pie pan and season with salt and pepper.
Pour enough olive oil into a 10 or 12 inch frying pan to reach a depth of 1/4 inch and heat it over medium-high heat.
Working with a few slices at a time, dip the eggplant into the edd, let the excess egg drip off and the slide the pieces into the hot oil.
Cook on each side just until golden brown then remove and drain on paper towels or brown paper bags. (Watch the eggplant carefully; the thin slices will cook very quickly.).
Layer the eggplant and Marinara Sauce in a shallow baking dish, ending with a film of sauce on top.
Sprinkle the cheese evenly over the sauce and bake for 10 minutes.
Serve hot or at room temperature.