Combine the ingredients for the brine and bring to a simmer in a stock pot. After the mix boils, chill completely, then immerse the lamb in the brine and weight it down in a container large enough to fit the ham. Keep the leg of lamb in the brine for 6 days, then remove.
Remove the lamb from the brine and chill overnight, uncovered (optional). Before smoking, lightly score the surface with ¼ inch crosshatches using a sharp paring knife. Transfer the lamb to a 200F smoker for 3 hours. From here, the ham can be chilled until the day it will be served, and will keep refrigerated for 5 days.
To serve the ham, heat the ham in a 225 degree oven for 1.5 hours or until a hot throughout, or until a thermometer reads 150 F. Whisk together the ingredients for the glaze, then baste the ham while it cooks as often as you can remember, preferably using a brush.
When it’s time to serve, turn the heat up to 450, basting every 10 minutes, for 30 minutes, or until a rich, glossy glaze has formed. Allow the lamb to rest for 15-20 minutes while you heat up any side dishes, then bring to the table, carve and serve.
Lamb or goat shoulder can be smoked just like a ham, but will have slightly more fat.