Preheat oven to 400°F. Lightly coat a large rimmed baking sheet with cooking spray. Place eggplant in an even layer on prepared baking sheet; brush 1 side with 1 Tbs. oil. Season with the salt and pepper. Bake until tender, about 15 minutes. (Do not turn oven off.)
Meanwhile, heat garlic and remaining 2 Tbs. oil in a small skillet over medium, stirring, until fragrant, about 2 minutes. Brush garlic oil onto cut sides of rolls, and place, cut sides up, on a large rimmed baking sheet. Turn oven to broil with oven rack 8 in. from heat.
Broil rolls until lightly toasted, 1 to 2 minutes. Remove from oven. Divide eggplant slices evenly among rolls. Spoon marinara sauce over eggplant slices and sprinkle evenly with mozzarella and Parmesan cheeses. Return to oven, and broil until cheese is melted, 2 to 3 minutes. Garnish with basil. Serve immediately.
