Peel and thinly slice 2 inches of the ginger. Remove the rosemary leaves from the stem. Add the ginger, rosemary, orange juice, honey, sugar, and soy sauce to a medium saucepan and bring to a simmer. Let cook about 10 minutes to slightly thicken.
Preheat oven to 350 F and prepare a baking dish with a roasting rack. You may want to layer the oven with foil in case of fat splatter.
Remove the neck and giblets, and rinse the duck. Pat it dry, then remove excess fat from the neck cavity and tail area. Using a sharp paring knife, prick the skin everywhere but the drumsticks (without going so deep as to prick the meat) to give the fat a way to drip out.
Peel 1 inch of the ginger, then grate or very finely chop. Mix this with the salt, pepper, and paprika. Rub this over the outside of the duck, and sprinkle remaining mix in the cavity. Place the orange slices in the cavity along with the rosemary.
Trim or tuck the wings, close the neck cavity with a skewer, and tie the legs together. Roast duck for a total 22 minutes per pound.
While it's roasting, every 30 minutes, remove the duck from the oven. Tilt the duck so that the juices in the cavity pour into the baking dish. Transfer the duck to a plate, then pour the drippings from baking dish into a heat resistant bowl or measuring cup. Return the duck to the roasting pan, flipped. Brush on glaze before returning to the oven.
When done, remove from oven and brush with one last coat of glaze, then let rest 15 to 20 minutes.
Carve, and serve warm along with your favorite sides.