Cut the ends off the eggplant, then cut into thin slices. Discard the smaller pieces that are mostly covered in skin. You'll want to end up with about 8 slices.
Slice the tomato and mozzarella thinly as well. Julienne the basil leaves.
Heat up a griddle or grill pan. Brush the eggplant slices with olive oil, then grill for a few minutes on each side.
When the eggplant softens and you are almost done cooking the second side, add some mozzarella and tomato slices on top.
Sprinkle on some basil, drizzle on a little olive oil, and season with salt and pepper.