Step 1

Heat a large skillet over medium. Add chiles; cook, stirring occasionally, until toasted and beginning to blister, 3 to 4 minutes. Remove from heat. Transfer chiles to a bowl; let cool slightly, about 5 minutes. Transfer chiles to a spice grinder, and grind into a coarse powder. Alternatively, grind chiles using a mortar and pestle. Stir together brown sugar, salt, paprika, granulated garlic, onion powder, cumin, black pepper, cayenne, and ground chiles in a medium bowl until well combined; set aside.

Step 2

Rub pork shoulder all over with mustard, ensuring entire shoulder is evenly coated. Sprinkle evenly with brown sugar mixture, gently pressing mixture into pork to adhere. Let stand at room temperature while preparing smoker, about 30 minutes.

Step 3

Prepare charcoal fire in smoker to indirect heat according to manufacturer's instructions. Place 3 or 4 large applewood chunks on coals. Maintain internal temperature at 240°F to 260°F for 15 to 20 minutes. Smoke pork over indirect heat, covered with smoker lid, until a thermometer inserted into thickest portion of meat registers 155°F to 165°F, 5 to 6 hours. Remove pork from smoker, and wrap tightly in butcher paper or aluminum foil. Return pork to smoker, and smoke until a thermometer inserted into thickest portion of meat registers 195°F to 200°F, 2 to 3 hours, checking temperature of meat and smoker each hour and adding more hot coals to smoker as needed to maintain internal smoker temperature of 240°F to 260°F. Remove pork from smoker, and let rest at room temperature, wrapped in butcher paper or foil, for 20 minutes. Unwrap pork. Remove and discard shoulder blade. Using tongs or gloved hands, gently shred and pull pork apart. Serve immediately.