Heat the grill to medium-high. Brush both sides of the eggplant slices with olive oil and sprinkle with salt. Add slices to grill rack. Grill for 3 minutes. Flip the eggplant rounds.
Top 4 of the slices with the mozzarella cheese. Grill all slices 3 minutes more. Remove from grill rack. Add plain eggplant slices to the cheese-topped slices to make 4 stacks. Top each stack with 2 tablespoons sauce, 1 teaspoon Parmesan, and 1/2 tablespoon basil.