Duck À l’Orange

Score the duck breasts: arrange a breast skin side up. Using a sharp knife, make diagonal incisions spaced 1⁄4" apart through the duck fat without piercing the flesh. Turn the duck breast 45˚ and cut crosswise incisions spaced 1⁄4" apart to make a diamond pattern. Repeat with remaining breast; put duck breasts in a small bowl.

Using a peeler, peel 2 oranges; juice them into a bowl (you should have about 2⁄3 cup of juice). Julienne the peel. Add half the peel and 1⁄3 cup of the juice to the duck breasts along with 1 tsp. sugar; toss duck breasts to coat, cover with plastic wrap, and refrigerate for 4 hours or overnight. Set the remaining orange juice and peel aside.

Arrange a rack in bottom third of oven and heat oven to 325˚. Season duck legs with salt and pepper. Using a cleaver, chop the duck carcass into 3" pieces. Heat a 3-qt. high-sided skillet over medium heat. Put in duck legs skin side down; cook until browned, about 15 minutes. Transfer duck legs to a plate. Add duck carcass to skillet and cook, turning, until browned, 10-12 minutes. Pour off and reserve all but 1 tbsp. duck fat from pan, keeping the carcass in pan. Add carrots and onions to the carcass and cook, stirring, until browned, about 10 minutes. Add chicken stock, peppercorns, parsley, thyme, and bay leaves to the skillet. Bring to a boil; nestle in duck legs skin side up; bake, covered, until duck legs are tender, 40-45 minutes.

Transfer duck legs skin side up to a 10" skillet, pat dry, and brush with 2 tbsp. of the reserved fat; set aside. (Reserve remaining duck fat for another use.) Strain broth into a 2-qt. saucepan; discard solids. Simmer, skimming off fat, until reduced to 2 cups, 25-30 minutes. Add vinegar along with the remaining orange juice, orange peel, and sugar and simmer until sauce coats the back of a spoon, about 30 minutes. Remove pan from heat and whisk in butter. Adjust the seasoning of the sauce with more salt and vinegar, if you like. Keep sauce warm.

Meanwhile, heat a 10" skillet over medium heat. Drain duck breasts. Brush off marinade, pat dry, and season with salt and pepper. Put duck breasts skin side down in skillet and cook, occasionally pouring off fat, until skin is crisp and golden brown, 20-25 minutes. Flip duck breasts and cook until medium rare, about 1 minute more. Transfer duck breasts to a cutting board and let rest 5 minutes.

Increase oven heat to broil; position a rack 8" from element. Broil reserved duck legs until skin crisps, 3-5 minutes. Thinly slice breasts crosswise. Arrange breasts and legs on a platter; pour sauce over top. Garnish with orange segments and parsley.