Ingredients

• 1 1/2 pounds tomatoes, chopped
• 2 tablespoons extra-virgin olive oil
• 1 medium onion, chopped
• 5 garlic cloves, chopped
• 1/4 teaspoon hot red pepper flakes
• 1/3 cup grated Parmigiano-Reggiano
• 4 (6-inch) hero or hoagie rolls, split
• 1/4 cup extra-virgin olive oil, divided
• 2 (1-pound) eggplants
• 1/2 pound thinly sliced provolone or fresh mozzarella, divided
• 1 cup basil leaves, chopped

Instructions

1. Purée tomatoes in a blender until very smooth. Heat oil in a 3-to 4-quart heavy saucepan over medium-high heat until it shimmers. Sauté onion and garlic with red pepper flakes until golden, about 4 minutes. Add tomato purée, 1/2 teaspoon salt, and 1/4 teaspoon pepper and simmer, uncovered, stirring occasionally, until thickened, 30 to 35 minutes. Remove from heat and stir in cheese.
2. Prepare grill for direct-heat cooking over medium-hot charcoal (medium-high heat for gas); see Grilling Procedure .
3. Brush cut side of rolls with 1 tablespoon oil total.
4. Cut eggplants crosswise into 1/2-inch-thick slices. Brush both sides of slices with remaining 3 tablespoons oil and season with 1/2 teaspoon salt.
5. Oil grill rack, then grill eggplant (covered only if using a gas grill), loosening with a metal spatula and turning occasionally to avoid overbrowning, until very tender, 6 to 8 minutes. Top eggplant (still on grill) evenly with half of sliced cheese, then grill, covered, until cheese begins to melt, about 30 seconds. Transfer eggplant with spatula to a large tray.
6. Grill rolls (cut side only) until grill marks appear, about 1 minute, and transfer to tray.
7. Transfer grilled rolls to 4 plates and spoon about 3 tablespoons tomato sauce onto each bottom piece. Top with eggplant, making 2 layers. Add remaining sauce, then top with basil and remaining cheese and close sandwiches.