In a small bowl, combine the brown sugar, smoked paprika, garlic powder, onion powder, salt, black pepper, and cayenne pepper. Mix them thoroughly until the rub is well blended. Pat the pork shoulder dry with paper towels and apply the rub generously to all sides of the meat, pressing it in to ensure it sticks.
Place the seasoned pork shoulder into the basin of your slow cooker. Pour the apple cider vinegar and the water (or chicken broth) around the sides of the pork, being careful not to wash off the spice rub from the top of the meat. The liquid provides the moisture needed to keep the pork tender during the long cooking process.
Cover the slow cooker with its lid and set it to “Low.” Cook the pork for 8 to 10 hours. Cooking on low is essential for breaking down the tough connective tissues in the pork shoulder. If you are in a hurry, you can cook it on “High” for 5 to 6 hours, though the low setting yields the most tender results.
Once the pork is fork-tender, remove it from the slow cooker and place it on a large cutting board or in a shallow bowl. Use two forks to shred the meat into bite-sized pieces, discarding any large chunks of excess fat. The meat should pull apart effortlessly at this stage.
Drain most of the liquid from the slow cooker, leaving about half a cup for moisture. Return the shredded pork to the pot and stir in the BBQ sauce. Toss the meat until it is evenly coated. Let it sit on the “Warm” setting for another 15-20 minutes to allow the flavors to meld before serving.