Step 1: Pat the pork shoulder dry with paper towels. Trim off any excessively thick fat, leaving a thin layer for moisture.
Step 2: In a small bowl, combine brown sugar, smoked paprika, garlic powder, onion powder, chili powder, black pepper, and kosher salt to create the dry rub.
Step 3: Generously rub the spice mixture all over the pork shoulder, ensuring full coverage. Cover and refrigerate for at least 4 hours, or preferably overnight.
Step 4: When ready to cook, place the rubbed pork shoulder in a large slow cooker (fat-side up if possible).
Step 5: Pour the apple cider vinegar and chicken broth around the pork in the slow cooker.
Step 6: Cover the slow cooker and cook on LOW for 8-10 hours, or until the pork is fork-tender and easily shreds (internal temperature should be 200-205°F / 93-96°C).
Step 7: Carefully remove the pork from the slow cooker and transfer it to a large cutting board or platter. Tent loosely with foil and let it rest for 20-30 minutes.
Step 8: Using two forks or meat claws, shred the pork, discarding any large pieces of fat or bone. You can moisten the pulled pork with a few spoonfuls of the cooking liquid from the slow cooker.
Step 9: Serve the pulled pork hot with your favorite barbecue sauce, either mixed in or on the side, on buns, tortillas, or as desired.