Preheat outdoor or indoor grill or oven broiler. In a medium bowl, combine cheeses and basil; set aside.
Place eggplant slices on a lightly greased grill and cook for 4 to 5 minutes; turn and cook for another 4 to 5 minutes.
Top eggplant with tomato slices and cheese/basil mixture; cover lightly with foil wrap and grill for 2 minutes or until cheese has melted.