1 beef brisket, 4-5 lbs. (2-2.5 kg), trimmed of excess fat
3 cloves garlic, cut into slivers
2 tbsp. vegetable oil
1 tbsp. coarse or kosher salt
1 1/2 tsp. dried thyme
1 tsp. freshly ground pepper
1 tsp. paprika
1 tsp. cayenne pepper
Basic barbecue sauce

Make several slits in the surface of the brisket and poke a sliver of garlic into each one. Rub the brisket with the oil. In a small bowl stir together the salt, thyme, pepper, paprika and cayenne pepper and rub over the meat.

Prepare a fire for indirect-heat cooking in a covered grill. Position the oiled grill rack 4-6 inches (10-15 cm) above the fire. Place the brisket on the rack so it is not directly over the coals, cover the grill and cook for 1 hour, turning once. Brush with some of the sauce and cook 1-1 1/4 hours longer, turning and brushing lightly with sauce two or three times more.

Remove from the grill and let rest for 10 minutes. Carve into thin slices across the grain. Arrange on a warmed platter and spoon a little sauce over the top. Pass the remaining sauce in a bowl at the table. Serves 8-10.