For the Duck and Duck Jus

1 whole pekin duck (about 5 lbs.)
3 medium carrots, trimmed and finely chopped
1 medium yellow onion, finely chopped
1 rib celery, finely chopped
1 cup red wine, preferably merlot or zinfandel
4 pekin duck breast halves (about 1 1⁄3 lbs.)
Salt and freshly ground black pepper
3 Tbsp. sunflower oil
¹⁄₄ cup cold butter, cut into 1⁄4" cubes

For the Green Beans

³⁄₄ lb. green beans, trimmed and thinly sliced lengthwise on the diagonal
³⁄₄ cup vegetable stock
¹⁄₄ cup butter
Salt and freshly ground black pepper

Instructions

For the duck and duck jus: Remove breast halves (leaving bones attached to carcass), legs, and excess fat from whole duck (discard fat or render it for cooking and reserve legs for another use). Refrigerate breast halves. Chop duck carcass with a butcher's cleaver into 8–9 large pieces and transfer to a large stockpot. Add carrots, onions, celery, and 8 cups water to pot and bring to a boil over medium-high heat. Skim off and discard any foam that rises to surface, reduce heat to medium-low, and simmer, partially covered, for 6 hours. Strain stock through a fine sieve, discarding solids. Set aside to let fat rise to surface, 15–20 minutes. Skim off and discard fat. Put wine into a small pot over medium heat and reduce to 2 tbsp., about 10 minutes. Add stock and cook until liquid has reduced to 1 cup, 7–8 minutes. Set duck jus aside.
Preheat oven to 350°. Score skin on the 6 duck breast halves (2 from duck and 4 additional) in a crisscross pattern with a very sharp knife, cutting halfway through skin. Season with salt and pepper. Heat oil in a large skillet over medium heat. Working in 2 batches, cook duck breasts in skillet, skin side down, until just golden brown, about 1 1⁄2 minutes. Reduce heat to medium-low and cook until deep golden brown, 8–10 minutes. Transfer breasts, skin side up, to a rack on a baking sheet and roast until medium rare, 8–10 minutes. Set aside to let rest.
Meanwhile, bring duck jus to a boil over medium heat. Add butter 2–3 pieces at a time, whisking constantly, until incorporated. Reduce heat to medium-low and simmer until jus thickens, 6–7 minutes. Keep jus warm.
For the green beans: Put beans, vegetable stock, and butter into a small pot, cover, and cook over medium-high heat for 2 minutes. Uncover and cook, stirring constantly, until liquid has thickened and beans are softened, 6–7 minutes. Season to taste with salt and pepper.
To assemble: Cut duck breasts crosswise on the diagonal into 1⁄2"-thick slices. Spoon a little of the jus onto 6 plates, top each with duck, and divide beans between plates. Serve immediately.