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1
In a heavy skillet cook the onion in the oil over moderately low heat, stirring, for 3 minutes, stir in the garlic, and cook the mixture, stirring, until the onion is softened.
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2
Add the tomatoes, the sugar, and salt to taste and cook the mixture over moderate heat, stirring, for 20 minutes.
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3
Force the mixture through the fine disk of a food mill set over a saucepan and cook the sauce over moderately high heat for 5 to 10 minutes, or until it is thickened to the desired consistency.
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4
With a hand-held slicing device or large sharp knife cut the eggplant lengthwise into 1/4-inch slices.
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5
Sprinkle the slices on both sides with salt and let them drain in a colander for 30 minutes.
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6
In a bowl stir together the mozzarella, the goat cheese, and the shredded basil.
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7
Pat the eggplant dry, arrange one layer of it on the oiled rack of a broiler pan, and brush it with some of the oil.
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8
Broil the eggplant under a preheated broiler about 4 inches from the heat for 3 to 4 minutes, or until it is golden.
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9
Turn the eggplant, brush it with some of the remaining oil, and broil it for 3 to 4 minutes more, or until it is golden.
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10
Transfer the eggplant to a large platter to cool and broil the remaining eggplant, brushing it with the remaining oil, in the same manner.
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11
Spread a mounded teaspoon of the cheese mixture lengthwise down the middle of each eggplant slice, leaving a 1-inch border at the wide end, and, beginning at the narrow end, roll up the eggplant jelly-roll fashion.
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12
Arrange the rolls, seam sides down, in an oiled flameproof shallow baking dish just large enough to hold them in one layer and broil them for 3 minutes, or until the cheese is just melted and bubbling.
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13
Transfer the eggplant rolls with a spatula to serving plates, spoon the tomato sauce over them, and garnish the rolls with the basil leaves.
