Cut eggplants in very thin slices.Heat ½ olive oil in a skillet and fry eggplant slices, carefully, on both sides, until lightly golden. Drain in paper towel and reserve.
Arrange slices, in one layer, on 4 – 6 dishes, covering the surface. Sprinkle salt and pepper and pour remaining olive oil and lemon juice over slices. Scatter parmesan slices on top.
Decorate with cherry tomatoes and chopped parsley.