Preheat oven to 375 F. Coat a 13×9 baking dish with olive oil. Heat 2 tablespoons olive oil in a large skillet over medium-high heat. Add onion, pepper and garlic and cook for 2 minutes. Add tomatoes and cook for 5 minutes, stirring often. Add the remaining sauce ingredients and turn heat to low. Cover the pan and simmer for 15 minutes.
Meanwhile, heat grill to medium-high. Brush the eggplant with olive oil and season with salt and pepper. Grill for 1-2 minutes per side, or until grill marks form and the eggplant is lightly softened. Transfer to a plate.
Place a layer of eggplant in the prepared baking dish and top with basil, sauce and cheese. Repeat the layer 1 more time. Finish with a drizzle of olive oil. Bake (covered with foil) for 20 minutes. Remove foil and bake for 15 minutes longer, or until cheese is bubbly. Let sit 10 minutes before slicing. Serves 8.