Make the Spice Rub: Mix together brown sugar, smoked paprika, garlic powder, onion powder, chili powder, cumin, black pepper, and salt. Rub generously all over the pork shoulder, covering all sides.
Set Up the Slow Cooker: Place the quartered onion and smashed garlic in the bottom of the slow cooker. Set the seasoned pork on top, fat side up. Pour the chicken broth and apple cider vinegar around the sides of the pork.
Cook Low and Slow: Cover and cook on LOW for 8–10 hours or HIGH for 5–6 hours, until the pork reaches 200–205°F internally and shreds easily with a fork.
Shred the Pork: Remove pork and transfer to a cutting board. Discard the bone and any large fat chunks. Strain and reserve the cooking liquid. Shred the pork into bite-sized pieces using two forks.
Sauce It Up: Pour the BBQ sauce over the shredded pork and toss to coat. Add a few tablespoons of reserved cooking liquid if needed for extra moisture.
Serve: Pile on brioche buns with coleslaw and pickles, or use in tacos, nachos, baked potatoes, and more.