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1
Puree tomatoes in a blender until very smooth. Heat oil in a 3-to 4-quart heavy saucepan over medium-high heat until it shimmers. Saute onion and garlic with red pepper flakes until golden, about 4 minutes. Add tomato puree, 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.
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2
Prepare grill for direct-heat cooking over medium-hot charcoal (medium-high heat for gas); see
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3
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4
Brush cut side of rolls with 1 tablespoon oil total.
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5
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.
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6
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.
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7
Grill rolls (cut side only) until grill marks appear, about 1 minute, and transfer to tray.
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8
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.
