Thoroughly coat a roasting pan and rack with nonstick spray.
Cut 4 slices from the center of the orange for garnish and refrigerate until ready to serve. Cut the remainder of the orange into wedges and set aside.
Remove the neck, giblets, liver and heart from the cavity of the duck and reserve for another use or discard.
Trim away any flaps of excess skin from around the cavity and tail area. Rinse the duck in cool water and pat dry with paper towels inside and out.
Season the duck's cavity with kosher salt and freshly ground black pepper, then stuff with the orange wedges and rosemary sprigs.
Bend the wing tips under the bird and tie the legs together with cotton twine. Place the duck, breast side up on the prepared roasting rack.
If you're able, prepare the duck to this point and refrigerate uncovered overnight. This will help to dry the skin, making for a crispier end result.
Set the duck aside for 1 hour to allow it to come to room temperature (do not cover).
Preheat the oven to 350°F.
Using the tip of a sharp knife, prick the skin of the duck all over (1/4-inch spacing), being careful not to pierce all the way through to the meat.
Rub kosher salt and pepper all over the duck, top and bottom, then place it in the oven and roast for 30 minutes.
Remove the duck from the oven, turn it breast side down on the rack and continue roasting. It's a good idea to rotate the pan in the oven as well to ensure even browning.
Repeat this process every 30 minutes until an instant-read thermometer inserted in the thickest part of the duck's thigh registers 165°F. Total cooking time should be about 2-1/2 hours.
Once cooked, tilt the duck to drain the fat and juices that have accumulated in the cavity into the roasting pan. Tent loosely with foil and allow it to rest for 10 to 15 minutes before carving.
While the duck rests, prepare the sauce. Combine the orange juice, rosemary and mustard in a small saucepan and bring to a rapid simmer over medium-high heat.
Cook, uncovered, until reduced to about 1/2 cup, 6 to 8 minutes.
Remove from the heat, add the vinegar, butter and orange zest and stir until the butter has melted. Season to taste with salt and pepper.
To serve, transfer the carved duck to a serving platter and garnish with fresh orange slices and sprigs of rosemary. Drizzle with sauce and serve immediately.
Tips for Making This Recipe
Everyone's oven is different, so if you find that you’re getting too much browning on some areas of the skin, shield them with foil.
Rotate the pan every time you turn the duck. This helps for even browning.
Coat your racks very thoroughly with nonstick spray to make turning the duck over as easy as possible. If you can, re-coat the rack every time you turn the duck. You don’t want to have any of that lovely, crispy skin stick to the rack!
How to Make Spiced Pomegranate Sauce (recipe variation)
2 tablespoons butter, divided
2 teaspoons minced shallot
1/4 teaspoon ground allspice
1/4 teaspoon ground cinnamon
Pinch of ground ginger
3/4 cup pomegranate juice
1/4 cup orange juice
1 teaspoon lemon juice
1 teaspoon fresh lemon zest
Salt and freshly ground black pepper
Melt 1 tablespoon of the butter in a small saucepan over medium heat. Add the shallot and sauté until softened, 1-1/2 minutes. Sprinkle with the allspice, cinnamon and ginger.
Add the pomegranate and orange juices, increase the heat to medium-high and bring to a rapid simmer. Cook, uncovered, until reduced to about 1/2 cup, 6 to 8 minutes.
Add the lemon juice, lemon zest and remaining tablespoon of butter and stir until the butter has melted. Season to taste with salt and pepper. Serve warm. Makes 1/2 cup.