1 Cinnamon stick, broken into rough pieces
1/4 tsp whole cloves
13 cups apple cider
8 ice cubes
1 cured bone-in half ham, (7-10 pounds) preferably shank end
2 tbsp Dijon mustard
1 cup dark brown sugar
1 tsp pepper
Toast the cinnamon and cloves in a large sauce pan over medium heat until fragrant, about 3 minutes. Add 4 cups cider and bring to a boil. Pour spiced cider into a larger stockpot or bucket and add 4 more cups of cider and ice. Stir until ice is melted.
Meanwhile, remove the skin from the exterior of ham and trim fat to 1/4-inch thickness. Score remaining fat at 1 inch intervals in criss-cross pattern. Transfer ham to container with chilled cider mixture. (Liquid should nearly cover the ham) Refrigerate for at least 4 hours or up to 12 hours.
Discard cider mixture and transfer ham to a large oven bag. Add 1 cup fresh cider to bag, tie securely, and cut 4 slits in top of bag. Place in a large roasting pan and let sit at room temperature for 1 1/2 hours. Adjust oven rack to lowest position and heat oven to 300 degrees. Bake ham until internal temperature registers 100 degrees, 1 1/2 - 2 1/2 hours.
Meanwhile, bring remaining cider and mustard to boil in a saucepan. Reduce heat to medium-low and simmer, stirring often, until mixture is very thick and reduced to 1/3 cup, about 1 hour.
Combine sugar and pepper in a a bowl. Remove ham from oven and let rest for 5 minutes. Increase oven temperature to 400 degrees. Roll back oven bag and brush ham with reduced cider mixture. Carefully press sugar mixture onto the ham. Return to oven and bake until dark brown and caramelized, about 20 minutes. Transfer to cutting board and loosely tent with foil, let rest 10 minutes.