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1
Brine ham: 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.
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2
Remove from heat and add ham.
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3
(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.
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4
Prepare grill for cooking using enough hardwood charcoal to fill a charcoal chimney or a shoe box.
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5
When coals are ready, push them to one side of grill, leaving about two thirds of grill without coals.
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6
Put a drip pan opposite coals.
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7
Make spice rub and cook ham: Finely grind all spice-rub ingredients together in an electric coffee/spice grinder.
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8
Drain ham and pat dry.
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9
Rub ground spices all over ham.
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10
Place ham on grill rack, fatty side up, over drip pan.
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11
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.
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12
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 155u00b0F, 1 to 2 hours more.
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13
Make glaze while ham is grilling: Heat glaze ingredients over moderate heat, stirring, until butter is melted.
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14
During last 30 minutes of grilling, brush ham with glaze several times, letting excess fall into drip pan.
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15
Serve ham: Transfer cooked ham to a platter and cover loosely with foil.
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16
Let ham stand 30 minutes to 1 hour before carving.
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17
Serve with pan drippings (skimmed of fat).
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18
Cooks' notes:
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19
Gas grill method: Preheat grill to moderately low.
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20
Place ham, fatty side up, in grill on a rack in a large broiler pan.
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21
Close lid, then roast about 3 hours.
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22
Oven method: Roast ham, fatty side up, on a rack in a large roasting pan in a preheated 350u00b0F oven, about 3 hours.
