Brush eggplant slices and sweet pepper pieces with 2 tablespoons of the olive oil. Sprinkle with salt and pepper.
For a charcoal grill, grill eggplant and sweet pepper on rack of an uncovered grill directly over medium coals for 8 minutes or until tender, turning once. (For a gas grill, preheat grill. Reduce heat to medium. Place eggplant and peppers on rack over heat. Cover; grill as above.) Cool to room temperature.
On individual plates layer tomato slices, mozzarella slices, prosciutto, eggplant, and sweet pepper with several basil leaves. Drizzle on remaining olive oil and vinegar. Makes 6 servings.