Heat a frying pan. Lay the duck pieces, skin side down, and cook over high heat until the skins are nicely browned. Flip to brown the other side.
Take the duck from the frying pan and arrange in a single layer, skin side up, in an ovenproof dish. Scatter the rosemary around the duck pieces.
In the rendered duck fat, sauté the onion, celery and carrot. Season with salt and pepper. Deglaze with the white wine. Boil for about a minute.
Pour the vegetables with all the liquid into the dish with the duck. Braise in the oven, uncovered, for one hour.
Take the duck out of the oven. Transfer to a platter and keep warm.
Make the gravy. Melt the butter in a small sauce pan. Add the flour, all at once, stirring vigorously to prevent lumps from forming. Cook the mixture over medium heat for about five minutes or until the flour starts to brown. Pour in the vegetables and juices in which the duck cooked. Stir. Add enough broth to get the consistency that you prefer. Season with salt, pepper and a bit of sugar for balance.
To serve: Make a bed of mashed potatoes. Lay the duck on top. Pour the vegetables and gravy over the duck and mashed potatoes. Sprinkle with chopped parsley and serve.
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