Place a rack in middle of oven; preheat to 475°. Whisk together 1 Tbsp. Diamond Crystal or 1¾ tsp. Morton kosher salt, 1 tsp. freshly ground black pepper, 1 tsp. ground coriander, and ½ tsp. ground cumin in a small bowl. Pat one 5–6-lb. whole Pekin duck, neck and giblets removed, dry and sprinkle inside and out with spice mixture. Cut 1 orange in half through the equator; cut one of halves into quarters. Stuff duck cavity with orange quarters along with 4 onion wedges (from 1 small onion, cut through root end into 8 wedges), 4 sprigs marjoram, 4 sprigs thyme, and 2 sprigs parsley.

Squeeze juice from remaining orange half into another small bowl. Add ½ cup dry white wine and ½ cup duck or chicken stock or low-sodium chicken broth and stir to combine. Set aside.

Spread out ½ medium carrot, halved lengthwise, ½ celery stalk, and remaining 4 onion wedges in a roasting pan. Place duck on top of vegetables and roast 30 minutes.

Reduce oven temperature to 350°. Remove roasting pan from oven and pour in reserved orange juice mixture. Return pan to oven and roast duck until an instant-read thermometer inserted into a thigh near the bone registers 170°, 1–1¼ hours. Remove from oven.

Heat broiler. Broil until duck skin is golden brown, about 3 minutes.

Using tongs, carefully tilt duck so juices run from cavity into pan. Transfer duck to a cutting board and let rest 15 minutes; set roasting pan with vegetables and juices aside.

While the duck is roasting, cook ⅓ cup sugar in a small heavy saucepan over medium heat, undisturbed, until starting to melt. Continue to cook, stirring occasionally with a heatproof rubber spatula, until sugar is fully melted and caramel turns deep golden in color. Reduce heat to low and carefully add ⅓ cup fresh orange juice and 2 Tbsp. white wine vinegar to caramel (mixture will bubble vigorously and might spatter); season with a pinch of kosher salt. Bring to a simmer and cook, stirring often, until caramel is dissolved and mixture is combined. Remove orange syrup from heat.

Remove vegetables from reserved roasting pan; discard. Pour pan juices through a fine-mesh sieve into a measuring glass; skim duck fat and reserve for another project. You should have 1 cup pan juices; if you don’t, add duck or chicken stock or low-sodium chicken broth to get you there.

Stir together 1 Tbsp. all-purpose flour and 1 Tbsp. unsalted butter, room temperature, in a small bowl to form a paste. Pour pan juices into a small heavy saucepan and bring to a simmer. Whisking constantly, add flour mixture followed by orange syrup and orange zest (from ½ orange, zest removed in wide strips with a vegetable peeler, strips thinly sliced). Simmer, whisking, until sauce is slightly thickened, about 5 minutes.

Serve duck with orange sauce alongside.