Preparation / Directions:
Rinse the olives under cold water.
Cut the duck into 4 pieces, 2 legs and 2 breasts. Using a towel, grab hold of the skin, and peel it off. (The skin is not used in this recipe. It can be kept to make crackling or discarded.) Remove the breast from the carcass, and cut each wing into 2 segments. Cut off the tips of each drumstick. Use of the gizzard is optional, but if using it, cut off and discard the silver skin surrounding it. (The 2 legs and 2 breast pieces should weight about 1 1/2 pounds; the 4 wing pieces, gizzard, liver, and heart should weight about 12 ounces.) Cut enough duck fat into 1/4-inch pieces so that you have 1 tablespoon of duck fat pieces.
Heat the tablespoon of duck fat until melted and hot in a large, sturdy saucepan. Add the wings and gizzard, and cook them over medium heat for 15 minutes, turning the duck pieces occasionally. Add the breasts and legs, and sprinkle the duck pieces with 1/4 teaspoon each of the salt and pepper. Brown the duck pieces on all sides over medium heat for 15 minutes. Transfer the duck to a plate.
Meanwhile, slice the fennel bulb in half and cut each half, into 1/4-inch slices. Place the fennel in the same saucepan you used to cook the duck, and add 1 cup water. Bring the water to a boil over high heat, then reduce the heat to low, cover, and cook gently for 6 to 8 minutes, until all the water has evaporated and the fennel is starting to brown.
Add the duck heart to the pan along with the remaining 1/4 teaspoon each salt and pepper, wine, vinegar and sugar. Cook over medium heat for 10 minutes.
Return the duck pieces to the pan, arranging them on top of the fennel. Bring to a boil, reduce the heat to very low, cover, and cook for 30 minutes. (The recipe can be prepared to this point up to 4 hours ahead.)
At serving time, add the olives and duck liver, and bring the mixture to a boil. Reduce the heat to low, cover, and warm over low heat for 15 minutes. Serve, sprinkled with the parsley, if desired.