Preheat oven to 425°F.
Slice the eggplant and tomatoes crosswise into ½-inch-thick pieces. Place 8 eggplant slices in a single layer on a baking sheet coated with nonstick cooking spray. Set the tomatoes aside.
In a small bowl combine the olive oil, vinegar, salt, and pepper. Brush the mixture over the eggplant and tomato slices, then set the remainder aside.
Bake the eggplant slices for about 10 minutes. Turn them over, brush with more of the olive-oil mixture, then bake for another 10 minutes; set aside. Place the tomatoes on the same baking sheet and cook for 2 to 3 minutes, or until they're soft.
Place a slice of cooked eggplant on a work surface. Top with a tomato slice, a basil leaf, a slice of mozzarella, a tomato slice, another slice of cheese, then a basil leaf. Finish the stack with a slice of eggplant. Repeat to make three more stacks.
When ready to serve return the stacks to the oven for about 5 minutes to reheat and melt the cheese. Top each with a drizzle of the remaining olive-oil mixture and a fresh basil leaf.