Preheat the oven to 500 degrees or an outdoor grill to high. Arrange the eggplant slices on paper towels. Salt both sides, then let drain for 10 minutes, turning once.
Combine the tomatoes with the onion and dress lightly with EVOO. Season with salt and pepper. Add the olives, capers and/or anchovies, if using.
Brush the eggplant with EVOO on both sides, then roast in a baking pan in the oven, or grill, covered, turning occasionally, until tender and browned, 10 to 15 minutes. Toast the rolls in the oven or on the grill until crisp, then rub the cut sides with the garlic and drizzle with EVOO.
Stack the eggplant, mozzarella and basil on the roll bottoms. Top with the tomato salad and roll tops.