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1
Have the butcher split the ducks lengthwise, remove and reserve the backbones and wingtips, and reserve the giblets.
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2
Chop the reserved backbones and wing tips into large pieces.
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3
Arrange the ducks skin side up in a large stainless steel or enameled baking pan and prick them all over with a skewer.
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4
Add the backbones and wing tips, the reserved giblets excluding the liver, the quartered onions, carrot, celery and garlic, and brown the mixture in a preheated very hot oven (550 degrees F)for 40 minutes, pouring the fat into a bowl periodically and reserve it.
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5
Transfer the ducks to a plate and pour any remaining fat into the bowl.
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6
Add 1 cup of the wine to the pan and reduce the liquid over moderately high heat by half.
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7
Add the stock, the cheesecloth bag, and the tomato paste and bring the liquid to a boil.
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8
Add the ducks, spoon some of the liquid over them, and braise them, covered tightly with foil, in a moderate oven (350 degrees F), basting them occasionally, for 40 minutes, or until they are tender.
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9
In a skillet, heat 3 tablespoons of the reserved duck fat over moderately high heat until it is hot.
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10
Add the potatoes with a pinch of sugar and salt and pepper, to taste.
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11
Saute them, turning, for 15 minutes, or until they are just tender, and drain them.
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12
In another skillet heat 2 more tablespoons of the reserved duck fat over moderately high heat until it is hot.
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13
Add the white onions with a pinch of sugar and salt and pepper to taste.
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14
Saute them, stirring, for 12 to 15 minutes, or until they are browned lightly and just tender, and drain them.
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15
Transfer the ducks to a plate and strain the cooking liquid into a stainless steel or enameled casserole.
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16
Return the ducks to the pan and roast them, uncovered, in a preheated hot oven (400 degrees) for 10 to 15 minutes, or until the skin is crisp.
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17
Skim the fat from the cooking liquid and reduce the liquid over moderately high heat to about 2 cups.
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18
In a small bowl, combine the remaining wine and the arrowroot, stir the mixture into the reduced cooking liquid, add salt and pepper to taste.
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19
Add the potatoes and onions and simmer the mixture for 5 minutes.
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20
Quarter the ducks, arrange them on a heated platter and spoon the vegetables over them.