Heat a grill pan on the stove or a grill press. Brush eggplant slices with 1 tbsp olive oil and season lightly with salt and pepper. Grill until marked and just soft, 4 to 6 min (turning once if using a grill pan).
Cut bread into 4 pieces; slice pieces or rolls in half lengthwise. Cover one side of each sandwich with tomato spread. Divide grilled eggplant between sandwiches, add cheese and top with other slices of bread.
Brush sandwiches with olive oil and rill until cheese is melting and bread is just crisp, 4 to 5 min.
Smoked cheese adds a delicious depth to this vegetarian meal.