2 small eggplants, cut crosswise into 1/4-inch slices
6 medium plum tomatoes, cut crosswise into 1/4-inch slices
1 teaspoon salt
1/4 teaspoon freshly ground black pepper
2 tablespoons extra-virgin olive oil
2 cloves garlic, minced
6 to 8 basil leaves, finely chopped, or about 1 teaspoon dried leaf basil
Fresh shredded Parmesan cheese