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1
Leave the eggplants untrimmed and cut them in half lengthwise through the stems.
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2
Lay the eggplant halves cut side down and, leaving the eggplants attached at the stem, make four evenly spaced cuts all the way down to the work surface that start just below the stem and run down to the tip of the eggplant.
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3
Sprinkle all the cut surfaces lightly with salt and rub them with 3 tablespoons of the olive oil.
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4
Lay the eggplant, cut side down and side by side, in a 13 x 9inch baking dish (or equivalent-size dish into which the eggplants fit comfortably).
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5
Cut the mozzarella and tomato slices in half.
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6
Tuck a half-slice of tomato and mozzarella in between the cuts in the eggplant.
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7
Season lightly with salt.
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8
Stir the bread crumbs and 3 tablespoons of the grated cheese together in a small bowl and sprinkle over the eggplants.
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9
Sprinkle the remaining 2 tablespoons grated cheese and the basil over the eggplants, and drizzle the remaining 1 tablespoon olive oil over them.
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10
Ladle the tomato sauce or broth between the eggplants and cover the dish with aluminum foil.
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11
Bake 20 minutes, uncover the dish, and continue baking until the eggplants are tender and the bread-crumb topping is golden brown, about 10 minutes.
