How to Make It
Prepare the grill for direct cooking over medium heat (350° to 450°F).
Brush the eggplant and tomato slices with oil and season evenly with salt and pepper. Brush the cooking grates clean. Grill over direct medium heat, with the lid closed as much as possible, until the vegetables are tender and nicely marked, turning once. The eggplant will take about 8 minutes and the tomatoes will take 2 to 4 minutes. Remove from the grill as they are done.
Divide the eggplants, tomatoes, cheese, and basil among four plates. Drizzle with a little more olive oil or your favorite salad dressing, if desired.