Wash Eggplant. Cut off ends and discard. Slice into 1/2-in slices, sprinkle with salt and place on paper towels. Let stand for 30 minutes. Preheat oven to 350 degrees. Gently shake excess moisture from eggplant slices and place on greased cookie sheet in a single layer. Bake approximately 30 to 40 minute turning once.
Cook whole potatoes and let cool. Peel and slice 1/2" thick. An alternative is to mash the potatoes and add a little milk to make a slightly creamy mashed potatoes.
For the meat sauce: Melt oil and margarine in a pan. Add meat, onions and garlic and brown. Add remaining ingredients and simmer on low for 20-30 minutes.
For the butter sauce: Melt margarine in saucepan, remove from heat and add flour, stirring to a smooth paste. Return to medium heat and slowly add milk, stirring constantly until sauce begins to bubble and thicken. Cook for 1-2 minutes. Whisk small amount of sauce into beaten eggs, then stir egg mixture into the pan of sauce. Add cheese, salt and pepper & mix well. Cook for 1-2 minute more until bubbles.
To put together: Spread thin layer of cream sauce over bottom of a 13x9x2-inch pan. Layer half of the eggplant slices and potato slices and top with all of the meat sauce. Place remaining eggplant and potato slices (or mashed potatoes) over meat sauce and spread remaining cream sauce over top. Sprinkle with additional parmesan cheese. Bake at 350 degree for about 1 hour or until browned on top.