Prep the pork shoulder
Pat the pork shoulder dry with paper towels and place it on a cutting board or shallow tray.
Make the dry rub
In a small bowl, combine the kosher salt, black pepper, smoked paprika, chili powder, brown sugar, garlic powder, onion powder, ground cumin, and crushed red pepper flakes (if using). Stir until evenly mixed.
Season the meat
Rub the spice mixture all over the pork shoulder, pressing it into all sides and crevices to coat the meat thoroughly.
Add liquid to the pot
Pour the chicken broth and apple cider vinegar into the bottom of a slow cooker (or a large Dutch oven if cooking in the oven).
Cook the pork
Place the seasoned pork shoulder into the slow cooker.
Cook on LOW for 8–10 hours, or until the pork is very tender and easily pulls apart with a fork.
(If using the oven, cover the Dutch oven tightly with a lid and bake at 300°F / 150°C for 4–5 hours, until fork-tender.)
Shred the meat
Transfer the cooked pork to a large cutting board or bowl and let it rest for about 10–15 minutes. Use two forks to shred the meat, discarding any large pieces of fat.
Sauce the pulled pork
Skim excess fat from the cooking juices, then pour about 1/2 to 1 cup of the juices over the shredded pork to keep it moist. Add 1 cup of barbecue sauce and toss until the meat is evenly coated. Taste and adjust seasoning with more salt, pepper, or barbecue sauce as desired.
Serve
Serve the pulled pork warm on toasted buns, in tacos, over rice, or alongside your favorite sides. Offer extra barbecue sauce on the side for drizzling.