Heat oven to 400° F. Place the eggplant on 2 rimmed baking sheets and brush with ¼ cup of the oil. Season with the cayenne and ¼ teaspoon salt and bake, turning once, until tender, 20 to 25 minutes. Let cool.
Meanwhile, mash the beans, garlic, tahini, lemon juice, the remaining tablespoon of oil, ¼ teaspoon salt, and ¼ teaspoon black pepper in a small bowl.
Divide the mashed beans, eggplant, red peppers, and romaine leaves among the bread.