Remove the rind and all but a thin layer of fat from the ham. Place the ham in a large baking dish or bowl. Cover with the apple cider and add 1 cup of the rum. Let stand at room temperature overnight.
Preheat an oven to 300° F. Remove the ham from the cider mixture. Reserve the cider mixture. Make diagonal cuts through the fat on the top of the ham to form a 1 1/2-inch grid. Stud a whole clove in the middle of each diamond. Place the ham on a wire rack fitted into a roasting pan. Add the marinade to the pan until it reaches the rack, but not the ham. Bake for 1 1/2, hours, basting every 20 minutes. Add more cider to the pan as needed.
Increase the oven temperature to 400° F. Combine the honey, brown sugar, and remaining 1 cup rum in a bowl. Whisk together to thoroughly combine. Spoon all of the glaze onto the ham, completely covering the surface and grid crevasses. Bake for 30 minutes. Remove from the oven. Let stand for at least 15 minutes or up to 45 minutes before carving and serving.Servings: 6 to 8