Creating the Grilled Eggplant and Tomato Stack is straightforward when you follow these steps:

1. Prepare Ingredients: Rinse and slice the eggplants into ½-inch thick rounds. Then, slice the tomatoes similarly.
2. Season Eggplant: In a bowl, mix olive oil, minced garlic, salt, and pepper. Brush this mixture onto both sides of the eggplant slices.
3. Preheat Grill: Heat your grill to medium-high temperature.
4. Grill Eggplant: Place the eggplant slices on the grill. Cook for about 4-5 minutes on each side, or until tender and grill marks appear. Remove from the grill and set aside.
5. Grill Tomatoes: If desired, grill tomato slices for 2-3 minutes on each side until they begin to soften and have grill marks.
6. Layer the Stack: On a serving platter, create layers starting with a slice of grilled eggplant, followed by a slice of tomato. Continue alternating until you’ve created stacks, ending with a tomato on top.
7. Drizzle Balsamic Vinegar: If using, drizzle the balsamic vinegar over the top of the tower for added flavor.
8. Garnish: Sprinkle fresh basil leaves and cheese, if desired, to finish the dish.
9. Serve: Allow the stack to cool slightly before serving, letting the flavors meld together.

These steps will ensure a successful and delicious outcome for your grilled dish.