Quintessential Italian ingredients like pesto and mozzarella share a starring role with eggplant in this heavenly sandwich. If you have a panini press, by all means use it to serve the sandwich at its crispy best!
Brush both sides of the eggplant slices with the olive oil and season lightly with salt and pepper. Grill the eggplant over a medium-hot fire, turning once, until tender, but not mushy, 5 to 7 minutes. Set aside at room temperature. At this point the eggplant can be refrigerated, covered, for up to 2 days; return to room temperature before proceeding with the recipe.
Spread the cut surfaces of the rolls with the pesto (1 tablespoon per roll). Arrange 2 slices of grilled eggplant on the bottom half of a roll, then top with tomato and 2 slices of mozzarella, and cover with the top of the roll; repeat with remaining ingredients. Serve immediately or grill on a panini press.