Preheat oven to 425°F (220°C). Use a sharp knife to score the duck skin in a 1-inch diamond pattern, being careful not to pierce the meat. Season the cavity and exterior generously with salt and pepper.

Stuff the duck cavity with quartered onion, half of the orange zest, thyme, and rosemary. Truss the legs with kitchen twine.

Place the chopped carrots and celery in a roasting pan. Set a rack over the vegetables and place the duck on the rack breast-side up. Roast at 425°F for 20 minutes to start the rendering process.

Reduce oven temperature to 350°F (175°C). Continue roasting for 1 hour and 15 minutes, or until the internal temperature at the thickest part of the thigh reaches 165°F (74°C). Drain rendered fat from the pan every 30 minutes.

While the duck roasts, prepare the gastrique: In a small heavy-bottomed saucepan over medium heat, melt the sugar until it turns a deep amber caramel. Carefully deglaze with vinegar, whisking until the caramel dissolves.

Add the fresh orange juice and duck stock to the gastrique. Bring to a boil and reduce by half (about 15-20 minutes).

Whisk in the cornstarch slurry and the remaining orange zest. Simmer for 2 minutes until thickened. Remove from heat and stir in the Grand Marnier and chilled butter cubes until glossy.

Increase oven temperature to 450°F (230°C) for the final 10 minutes of roasting to achieve maximum skin crispiness.

Remove duck from oven and let rest for 15-20 minutes before carving. Serve with the Bigarade sauce and fresh orange segments.