Heat the oven to 425°F. Toss eggplant with 2 tablespoons oil and its salt, spread on a rimmed sheet pan and roast for 22 to 25 minutes, turning once, until tender with browned edges.
Meanwhile, warm remaining oil in a saucepan and stir garlic for 30 seconds. Add tomatoes, water, oregano and pepper and simmer for 10 minutes.
Boil penne in water with the tablespoon salt until 3 minutes short of the package time, then drain. Lower the oven to 375°F.
Fold penne, roasted eggplant, olives and mozzarella cubes into the sauce. Transfer to a deep 9-by-13-inch baking dish and scatter with Parmesan.
Cover with foil and bake for 20 minutes, then uncover for 8 to 10 minutes until the center reaches 165°F and the surface browns lightly. Rest for 10 minutes before serving.