Preheat the oven to 400 degrees. Heat the oil in a nonstick skillet. Dip the eggplant in egg and fry the eggplant for about 3 to 4 minutes a side or until tender.
Set the eggplant slices on a baking pan and season each slice with salt and pepper. Spread each slice of eggplant with pesto and top with a slice of mozzarella cheese. Bake for 5 minutes or until the mozzarella melts.
Set one eggplant slice on top of the other if you wish, to form more of a towering sandwich and garnish with fresh basil leaves.