Combine all brine ingredients in a food-safe 5 gallon bucket. Whisk to dissolve. Add the ham to the solution. Weigh it down with plates to keep it submerged. Place in a refrigerator for 8 days, or a 1/2 day per pound.
Remove from brine. Rinse well under cold water. Place on a cooling rack, over a sheet pan. Place the ham in the refrigerator for 12 to 24 hours to form the pellicle (surface will become tacky).
Remove the ham from the refrigerator. Preheat your smoker to 250°F. Season the ham with the BBQ rub. Smoke for four hours. Increase the smoker's temperature to 350°F. Cook until an instant read thermometer inserted into the deep part of the meat reads 140°F.
Mix together the glaze ingredients in a bowl. Place the ham in a foil pan and place the pan in the smoker. Brush the glaze on the ham. Continue cooking until the internal temperature reaches 150°F. Glaze again. Continue cooking until the internal temperature reaches 155°F. Remove from the grill and let rest 30 minutes before slicing.