Whereas beef and pork barbecue are common in many regions of the United States, mutton is unique to several counties of western Kentucky, where it was once the most economical protein. Mutton or yearling mutton shoulder will have more flavor, but lamb is perfectly acceptable; mutton can be special ordered or found at halal and Latino markets.
Please read about Barbecuing. Trim all but ¼ inch of fat from:
Rub all over with:
Place on a rack set in a rimmed baking sheet and refrigerate, uncovered, overnight, or for up to 2 days.
Heat a smoker or grill set up for barbecuing to 225° to 250°F (preferably with a water pan). Add to the coals:
Add the brisket to the cooler side of the smoker or grill and cover so that the top vent pulls smoke across the meat. Adjust the vents to maintain the temperature (this is difficult and may take practice, or, in the worst case, a fresh load of charcoal). You may add another small chunk of hickory wood every hour for the first 4 hours. Baste the meat every 2 hours with:
Cook until the meat is tender and a thermometer inserted in the thickest part registers 200°F, 8 to 10 hours.
Transfer to a platter or baking sheet, cover with foil, and let the meat rest for at least 15 minutes. Meanwhile, put the remainder of the mutton dip in a small saucepan over medium heat and simmer for 5 minutes, or until thickened to your liking. Take the meat off the bone and thinly slice, pull, or chop it. Dress with enough sauce to lightly coat the meat (place the rest of the sauce on the table for use as a condiment). Serve as part of a “meat-and-three” (see Smoked Pork Shoulder). Or, to serve in sandwiches, provide: