- 4 quarts water
- 1 cup sugar
- 1 cup table salt
- 30 whole cloves
- 4 whole nutmegs, cracked
- 1 (8- to 10-lb) bone-in shank-end fresh ham, skinned and trimmed of all but a thin layer of fat
- 2 tablespoons plus 2 teaspoons coriander seeds
- 4 teaspoons cumin seeds
- 4 teaspoons whole black peppercorns
- 4 teaspoons paprika
- 4 teaspoons kosher salt
- 1/4 cup dark rum
- 1/4 cup molasses (preferably mildly flavored)
- 1/2 stick (1/4 cup) unsalted butter
- Bring all brining ingredients except ham to a boil in a deep 8- to 9-quart pot (such as a pasta pot), stirring occasionally until sugar and salt are dissolved. Remove from heat and add ham. (Brine should cover ham; if not, make more brine.) Cool mixture 30 minutes, then chill, covered, turning ham once or twice, at least 1 day and up to 2.
- Prepare grill for cooking using enough hardwood charcoal to fill a charcoal chimney or a shoe box. When coals are ready, push them to one side of grill, leaving about two thirds of grill without coals. Put a drip pan opposite coals.
- Finely grind all spice-rub ingredients together in an electric coffee/spice grinder.
- Drain ham and pat dry. Rub ground spices all over ham.
- Place ham on grill rack, fatty side up, over drip pan. Cover grill, leaving cover vents one fourth open and bottom vents fully open, and cook ham, adding a large handful of charcoal every 30 minutes. After 1 hour, turn ham around so other side faces coals and continue to cook until a meat thermometer inserted near but not touching bone registers 155°F, 1 to 2 hours more.
- Heat glaze ingredients over moderate heat, stirring, until butter is melted.
- During last 30 minutes of grilling, brush ham with glaze several times, letting excess fall into drip pan.
- Transfer cooked ham to a platter and cover loosely with foil. Let ham stand 30 minutes to 1 hour before carving. Serve with pan drippings (skimmed of fat).