Preheat oven to 375F. Grease a 1-1/2 quart baking dish.
Place the eggplant slices in a large pan with salt and 1" boiling water, Cover tightly and cook for 10 minutes. Drain well and mash.
To the mashed eggplant add eggs, melted butter, pepper, onion, basil and breadcrumbs; mix well.
Cover the bottom of the prepared dish with layers of half the eggplant mixture, then half the tomato slices and half the cheddar cheese. Repeat. Sprinkle Parmesan cheese over the top and bake for 45 minutes. Remove from oven and allow to rest for 10 minutes before serving.