Trim the pork of any silver skin and excess fat, but leave a thin layer for flavour. Brush the meat with mustard.
Mix all the dry rub ingredients together, then coat the pork thoroughly on all sides.
Soak apple wood chips in water for about 30 minutes. Preheat the grill to 120°C (250°F). For indirect grilling, turn off the middle burners and place the meat over them.
Insert a temperature probe into the thickest part of the meat to monitor the internal temperature. Set the probe target to 90°C (195°F). Drain the wood chips, place them in a smoker box, and position it over a lit burner.
Close the grill lid and smoke the meat for 3 hours (no peeking 🙂).
After this time, transfer the pork to a cast iron or steel roasting pan and increase the temperature to 135°C (275°F). Every hour, spray or brush the meat with the mixture of water, Worcestershire sauce, apple cider vinegar, and BBQ sauce to keep it moist and enhance the flavor.
When the internal temperature reaches 90°C (195°F), the pork is ready to be shredded. Use meat shredding claws or two forks to pull it apart into strands.
Lightly toast the burger buns on the warm grill. Spread with your favorite sauce, add a generous portion of pulled pork, and top with your favorite vegetables. Serve immediately and enjoy!