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1
Preheat the oven to 475.
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2
In a small roasting pan, spread half of the chopped onions, 1/4 cup of the parsley, 1 tablespoon of the thyme and the garlic, bay leaves and celery.
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3
Prick the duck skin all over with a fork and rub the duck with 2 teaspoons of salt, 1 teaspoon of black pepper and 1 teaspoon of herbes de Provence.
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4
Set the duck halves on the vegetables, cut sides down, and roast for 10 minutes.
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5
Prick the duck skin again, cover the pan with foil and reduce the oven temperature to 275.
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6
Roast the duck for about 3 hours longer, until the meat is very tender and most of the fat has rendered.
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7
Meanwhile, in a large skillet, cook the backbone, neck and wing tips over low heat until well browned all over.
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8
Add the remaining chopped onions and cook over moderate heat until browned, about 4 minutes.
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9
Pour off the fat from the skillet and add the tomato paste.
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10
Cook, stirring, until it begins to brown, about 3 minutes.
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11
Add the white wine and bring to a boil.
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12
Add the water, chicken stock and sugar and simmer until the stock is reduced to 1 cup, about 1 hour.
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13
Strain the stock and skim the fat from the surface.
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14
When the duck is tender, transfer the halves to a work surface.
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15
Halve each half; remove any vegetables, pockets of fat and loose bones.
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16
Transfer the duck pieces to a rimmed baking sheet, skin side up.
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17
Strain the juices from the roasting pan into a saucepan and skim off the fat; boil the strained juices until reduced to 1/4 cup.
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18
Add the strained stock and the olives to the saucepan and simmer for 10 minutes.
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19
Season the sauce with salt, pepper and herbes de Provence.
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20
Preheat the broiler.
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21
Season the duck with herbes de Provence, salt and pepper.
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22
Broil 10 inches from the heat for about 5 minutes, or until the duck is hot and the skin is crisp.
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23
Spoon the sauce onto a platter and set the duck on top.
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24
Sprinkle with the remaining 2 teaspoons of chopped parsley and 1 teaspoon of thyme and serve.
