Barbecue is a symbol of American ingenuity. It transforms cheap, tough cuts of meat into tender bites of heaven with nothing but time, smoke, heat, and a few spices. Serve this smoky pulled pork like they do in North Carolina--with some slaw on top of the sandwich.
Combine first 8 ingredients in a large bowl. Rub spice mixture onto pork; place pork in bowl. Cover and chill at least 8 hours or overnight. Soak hickory wood chips in water 1 to 24 hours.
Remove pork from refrigerator; let stand at room temperature 20 minutes. To prepare grill for indirect grilling, remove right grill rack. Preheat grill to low using both burners. After preheating, turn the left burner off (leave the right burner on). Maintain temperature at 225° to 250°. Drain wood chips. Place 1 1/2 cups wood chips on a 12-inch square of aluminum foil. Fold edges of foil to form a packet, and seal; pierce foil packet with a fork. Repeat procedure with remaining wood chips. Place 1 packet of wood chips on right side. Coat grill rack with cooking spray; place pork, fatty side up, on grill rack covering left burner. Cover and grill 8 to 10 hours or until a thermometer registers 190°. Replace packet of wood chips every 2 hours.
While pork cooks, combine cider vinegar and next 7 ingredients (through 1/2 teaspoon black pepper) in a medium microwave-safe bowl. Microwave at HIGH 2 to 3 minutes or until sugar dissolves, stirring every 1 minute. Cool to room temperature.
Combine coleslaw and 1/2 cup sauce in a large bowl; toss well. Cover and chill 1 hour.
Remove meat from grill; let stand 20 minutes. Shred meat with 2 forks; discard bone and fat. Combine shredded pork and 2 cups sauce in a large bowl; toss to coat. Spoon 3 ounces pork and 1/3 cup coleslaw on bottom half of each hamburger bun. Cover with top halves of buns. Serve with additional sauce for dipping.