Cut eggplant lengthwise into 6 (1/2-inch-thick) slices; sprinkle cut sides with salt. Place in a single layer on paper towels; let stand 1 hour.
Stir together garlic and olive oil; let stand 5 minutes.
Rinse eggplant with water, and pat dry. Brush eggplant and tomato with garlic mixture. Place eggplant in a single layer on baking sheets.
Broil eggplant 5 inches from heat (with electric oven door partially open) 3 minutes on each side; cool.
Place basil leaves on bread rounds. Top evenly with cheese, eggplant, and tomato. Drizzle with vinegar, and sprinkle with pepper. Roll up, and cut diagonally in half. Serve with salad greens, if desired.