Peel and thinly slice eggplant 1/8- to 1/4-inch thick.
Prepare tomato sauce from olive oil, tomatoes, onions, garlic, oregano, salt and pepper. Or buy prepared sauce.
In a shallow and wide bowl (wide enough to fit the eggplant slices horizontally) beat the 2 eggs, flour and water. Heat the oil in a skillet to medium heat (no smoke). Coat the eggplant slices in the egg mixture and sauté both sides until golden brown. This will take several rounds in the skillet to get all the slices sautéed, so just stack them up on a plate as they accumulate.
In a deep casserole dish place a thin layer of tomato sauce. Then make multiple layers of 1) eggplant, 2) tomato sauce 3) sprinkled Parmesan cheese, and 4) sprinkled mozzarella cheese, until all the eggplant is used.
Bake at 350 degrees for 30 minutes uncovered and 10 minutes covered with foil or casserole lid if available. Cool for 5 to 10 minutes, slice and serve hot.