"This is where patience has its rewards. When you barbecue pork shoulder slowly, until the internal temperature climbs near 190°F, the meat tears into shreds of pure satisfaction. If the outside gets dark, that's even better Barbecue aficionados call that the 'bark,' and its crispy texture is fabulous in combination with the rest of the meat." - Jamie Purviance
To make the rub: In a small bowl, mix the rub ingredients with your fingertips. Allow the roast to stand at room temperature for 20 to 30 minutes before grilling. Massage the rub mixture all over the roast.
Grill over indirect medium heat until the meat is very tender but still juicy (the internal temperature next to, but not touching, the bone should be 180° to 190°F), 5 to 6 hours, turning every hour or so. Add the soaked wood chips to the smoker box or coals about halfway through grilling time. When done, remove the pork shoulder from the grill, lightly cover with a piece of aluminum foil, and let rest for 30 minutes.
Meanwhile, make the sauce: In a medium saucepan, combine the sauce ingredients with 1 cup of water and bring to a boil over high heat, stirring occasionally. Reduce the heat to low and simmer for 10 minutes. Keep warm.
Pull the pork into shreds with two forks or your fingers, or chop it with a knife. Discard any outer sections that may have burned or any large bits of fat inside. In a large bowl, moisten the shredded meat with the sauce (you may not need all of it) and mix well. Serve warm on toasted buns brushed with mayonnaise.