Allow the ham to stand at room temperature for 30 to 40 minutes before grilling.
Prepare the grill for indirect cooking over medium heat (about 350° to 450°F).
Combine the glaze ingredients. Score the ham in a large crisscross pattern about ½ inch deep on all sides, except the cut side, and place it cut side down in a large disposable foil pan. Brush half of the glaze on the top and sides of the ham. Grill over indirect medium heat, with the lid closed, for 1 hour. Baste with the remaining glaze and continue grilling until an instant-read thermometer inserted into the thickest part of the ham (not touching the bone) registers 160°F, 45 minutes to 1½ hours more. If the glaze gets too dark, cover the ham loosely with aluminum foil for the remainder of the grilling time. Remove from the grill, tent loosely with foil, and let rest for 15 to 45 minutes.
In a nonreactive bowl whisk the sauce ingredients. Carve the ham and serve warm with the sauce.
