Light a grill.

Prepare the grill for indirect cooking: push the coals to opposite sides and set a drip pan in the center (or turn off the center burners on a gas grill).

Mix 3 tablespoons of coarse salt with paprika, brown sugar, garlic powder, and pepper in a bowl.

Rub the spice mixture all over the ham, concentrating on the meat.

When the fire is medium-low (275 to 300°F), add 1 1/2 cups of soaked wood chips to the coals (or smoker box in a gas grill).

Place the ham, skin side up, in the center of the hot grate above the drip pan.

Cover the grill and cook for 7 to 8 hours, replenishing coals every 1-2 hours and wood chips every hour for the first 4 hours.

Check for doneness with a meat thermometer; the internal temperature should reach 190°F.

If the ham browns too much, cover it loosely with aluminum foil for the last 2 hours.

Transfer the cooked ham to a cutting board.

Cover with aluminum foil and let rest for 20 minutes.

Pull off the crisp skin and chop it finely (optional).

Using gloves, pull the meat off the bones in large pieces and discard bones and fat.

Shred the pork using your fingers or two forks.

Transfer the pulled pork to a pan and stir in about 2 1/2 cups of vinegar sauce.

Season the pulled pork with salt and pepper.

If not serving immediately, cover the pan with foil and keep warm on the grill or in a low oven.

Lightly brush the cut sides of hamburger buns with melted butter.

Toast the buns on the grill.

Mound the pulled pork on the toasted buns, top with mustard slaw, and serve with vinegar sauce.