3 large eggplants, cut crosswise into 1/2-inch slices
¼ cup kosher salt, plus more for seasoning
2 tablespoon extra-virgin olive oil
2 tablespoons balsamic vinegar
freshly ground black pepper
16 slices large tomato, each 1/4-inch thick
1½ teaspoons minced garlic
1½ Lb fresh mozzarella, cut into 1/4-inch slices
In a large bowl toss eggplant slices with 1/4 cup kosher salt.
Using your fingertips, evenly distribute the salt on both sides of each slice.
Place eggplant slices in a colander set over a large bowl or sheet pan to catch juices. Set aside for 1 to 2 hours.
Preheat oven to 450F. Line two 18 by 13-inch baking sheets with heavy-duty foil.
Rinse the eggplant slices under cold water and pat dry thoroughly with paper towels.
Arrange the eggplant slices in a single layer on one baking sheet. Brush olive oil on 1 side.
Brush with balsamic vinegar and sprinkle with freshly ground pepper.
Drizzle the other pan with 2 tablespoons olive oil.
Bake the eggplant slices until they are tender and well browned, 20 to 30 minutes, without turning.
Arrange the tomato slices in a single layer, season with salt and pepper, then sprinkle with the minced garlic.
Roast the tomato slices until they are very soft and just beginning to brown, 10 to 15 minutes, without turning.
Let tomato and eggplant slices cool until you can handle them with your fingers.
Make a short stack starting with eggplant on the bottom, 1 slice mozzarella, and then tomato. Top with another piece of eggplant.
Keep Warm stacks in the oven until mozzarella lightly melts.
Drizzle with olive oil and serve.