Have ready in 3 separate bowls flour, eggs, and bread crumbs. Dredge eggplant in flour and coat with egg, letting excess drip off. Dredge eggplant in bread crumbs.
In a large heavy skillet heat 1/4 inch oil over moderately high heat until hot but not smoking and fry eggplant rounds in batches 3 minutes on each side, transferring them with a slotted spoon to paper towels to drain.
Preheat the broiler.
Arrange rounds on a baking sheet and top with tomato sauce and mozzarella. Broil rounds about 2 inches from heat until cheese is melted, about 3 minutes.