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Make sauce:
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Cook garlic and red pepper flakes in 1 tablespoon oil in a 2-quart heavy saucepan over moderate heat, stirring, until garlic is golden, about 30 seconds. Add tomatoes, sugar, and 1/2 tsp salt and simmer, uncovered, stirring occasionally, until slightly thickened, 15 to 20 minutes.
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Grill eggplant while sauce cooks:
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Heat grill pan over high heat until hot.
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Peel 2-inch-wide strips of skin from opposite sides of eggplant and discard. Holding a knife parallel to a peeled side, cut eggplant lengthwise into 8 (1/3-inch-thick) slices.
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Brush both sides of slices with 3 tablespoons oil (total), then season with salt and pepper.
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Grill slices in batches, turning over once and brushing grilled sides with some of remaining oil, until golden brown and tender, about 4 minutes, then transfer to a tray.
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Assemble eggplant rolls:
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Stir together cheeses, 2 tablespoons basil, pepper, and remaining salt.
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Divide cheese mixture among slices (3 to 4 tablespoons per slice), leaving an 1/8-inch border along edge.
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Roll up each slice, beginning with a short end, and serve rolls topped with sauce and sprinkled with remaining basil.