With a sharp knife, score parallel lines in a grid pattern, with cuts 1-inch apart and 1/4-inch deep, across the rounded, skin side of the ham.

In a large bowl, whisk the 1 cup of the sugar, orange juice, mustard, molasses, horseradish, cayenne, and 1/2 teaspoon of the allspice. Place the ham in a 2-gallon, plastic bag and pour the marinade into the bag. Gently squeeze the bag to evenly distribute the marinade around the ham. Place in a large bowl or baking dish and refrigerate for 24 hours.

Preheat the oven to 350 degrees F.

In a large mixing bowl, toss the potatoes with the vegetable oil, salt, cinnamon, remaining 1/4 teaspoon allspice, and remaining 2 teaspoons dark brown sugar. Layer the potatoes on the bottom of a Dutch oven or large, heavy roasting pan. Remove the ham from the marinade and place, scored-side up, on the potatoes. Bake for 45 minutes.

Pour the ham marinade into a 2-quart saucepan and bring to a simmer over medium-high heat. Reduce the heat to a bare simmer and cook uncovered until thick enough to coat the back of a spoon, about 20 minutes. Remove from the heat.

Remove the ham from the oven and evenly baste on all sides with the reduced marinade. Bake for 15 minutes. Remove the ham from the oven, baste again, and turn the sweet potatoes that can be reached. Return the ham to the oven and continue baking for an additional 1-1/2 hours, basting every 15 minutes, for a total cooking time of 2-1/2 hours.

Remove from the oven and let rest for 15 minutes before carving. Serve hot with the sweet potatoes