Pat the pork shoulder dry with paper towels. Rub the pork all over with yellow mustard.
In a small bowl, mix together the dry rub ingredients. Coat the pork shoulder generously, pressing the seasoning into every surface. Let it sit at room temperature while you preheat the smoker.
Preheat your pellet smoker to 225°F.
Place the pork shoulder directly on the smoker grates, fat side up. Close the lid and smoke until the internal temperature reaches 165°F—this usually takes about 4-5 hours.
Mist the pork with water or apple cider vinegar every hour to keep the bark moist. (optional)
Once the pork reaches 165°F and has a dark, flavorful crust, remove it from the smoker.
Place the pork in the Instant Pot and pour in the chicken broth or water.
Seal the lid and set the Instant Pot to Manual (Pressure Cook) – High Pressure for 45 minutes.
Allow a 15-minute natural release, then carefully vent any remaining pressure.
Carefully remove the pork from the Instant Pot—it will be fall-apart tender. Use two forks to shred the meat, discarding any large pieces of fat.
Toss the shredded pork in some of the cooking juices to keep it moist and flavorful. Stir in your favorite BBQ sauce, if desired.