In a small bowl, stir the olive oil and garlic together.
Brush both sides of the eggplant slices with 1 tablespoon of the garlic oil.
Put the eggplant in the grill; close the top plate, and cook until the eggplant is tender and grill marked, 3-5 minutes.
Season to taste with salt and pepper.
Transfer to a plate and set aside (the eggplant can be grilled up to 3 hours ahead and kept at room temperature, or covered and refrigerated for up to 24 hours; if refrigerating, return to room temperature before assembling the panini).
Keep the sandwich grill on and wipe clean the grill plates.
Place the rolls, cut side down, on a work surface and brush the crust sides of the rolls with the remaining 1 tablespoon garlic oil.
Turn and spread cut sides of the rolls with tapenade, dividing it evenly, then layer 1/4 of the cheese, half of the eggplant, and 2 tomato slices over the tapenade on the bottom half of each roll.
Divide the remaining cheese on top.
Cover with the top halves of the rolls, tapenade side down, and press to pack gently.
Place the panini in the grill, close the top plate, and cook until the bread is golden and toasted, the eggplant is hot, and the cheese is melted, 3-5 minutes.
Cut each sandwich in half on the diagonal and serve immediately.