Cut eggplant crosswise into 1/8-inch-thick slices.
Dip eggplant slices in egg, and dredge in breadcrumbs.
Pour oil to a depth of 1/8 inch in a heavy skillet. Fry eggplant in hot oil, in batches, 1 to 2 minutes on each side or until golden. Drain on paper towels, and keep warm.
Arrange eggplant on a serving dish; sprinkle evenly with cheese, and serve immediately.
