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1
Drain tomatoes, reserving juice, then finely chop. Heat oil in a 4- to 5-quart heavy pot over moderately high heat until hot but not smoking, then cook garlic, stirring, until golden, about 1 minute. Add tomatoes with reserved juice, water, tomato paste, sugar, and salt and bring to a boil. Reduce heat and simmer, uncovered, stirring occasionally, until thickened, about 30 minutes. Stir in basil.
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2
Bring a 5- to 6-quart pot of salted water to a boil over moderately high heat.
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3
Prick eggplants all over with a fork. Boil eggplants, uncovered, stirring occasionally, until tender when pierced with a knife, 20 to 25 minutes. Transfer with a slotted spoon to a colander to drain and discard cooking water. When eggplants are cool enough to handle (after about 15 minutes), halve eggplants lengthwise through stem (keep stem attached). With a small sharp knife, scoop out and reserve flesh, leaving 1/4-inch-thick shells. Very finely chop flesh and transfer to a large bowl.
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4
Bring rice and water to a boil in a 1-quart heavy saucepan, uncovered, then reduce heat and simmer rice, covered, until water has been absorbed and rice is tender, about 15 minutes. Remove from heat and let stand 5 minutes. Fluff rice with a fork and add to chopped eggplant.
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5
While rice cooks, combine bread and milk in a small bowl and let stand until bread has absorbed milk, then gently squeeze bread, discarding any milk.
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6
Add bread to rice mixture along with garlic, eggs, cheese, parsley, basil, 1/2 teaspoon salt, and 1/2 teaspoon pepper and stir to combine well.
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7
Sprinkle inside of eggplant shells with remaining 1/2 teaspoon salt and 1/2 teaspoon pepper. Firmly pack a scant 1/3-cup eggplant stuffing into each eggplant shell. (You may have some stuffing left over.)
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8
Put oven rack in middle of oven and preheat oven to 375u00b0F.
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9
Heat 1 inch vegetable oil in a 10-inch cast-iron or other deep heavy skillet over moderate heat until thermometer reaches 320u00b0F and add 2 eggplant halves, stuffing sides up. Fry, turning over once using 2 slotted spoons, until golden brown, 5 to 8 minutes total. Transfer, stuffing sides up, to paper towels to drain, then fry remaining eggplants, 2 halves at a time, in same manner, returning oil to 320u00b0F between batches.
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10
Spoon sauce into a 3-quart (about 13- by 9-inch) nonreactive baking dish. Add eggplants, stuffing sides up, and bake, covered with foil, until sauce is bubbling, about 25 minutes.
