Mix the spice rub. In a small bowl, combine brown sugar, smoked paprika, chili powder, cumin, onion powder, garlic powder, salt, and pepper.
Prep the pork. Pat the pork shoulder dry with paper towels.
Rub the spice mixture all over, pressing it into every crevice.
Build your base. Place sliced onions and minced garlic in the bottom of a Dutch oven (for oven method) or slow cooker. Add broth and apple cider vinegar. Stir in liquid smoke if using.
Choose your method. Oven: Nestle the pork into the pot, cover with a lid, and cook at 300°F for 3 1/2 to 4 1/2 hours, until the meat shreds easily with a fork.
Crock pot: Add the pork to the slow cooker, cover, and cook on Low for 8–10 hours or on High for 5–6 hours, until tender.
Shred and sauce. Transfer the pork to a large bowl.
Skim fat from the cooking liquid. Shred the pork with two forks. Add 1 cup of the cooking juices and 1 cup BBQ sauce.
Toss to combine and taste. Add more sauce or juices as needed.
Finish and serve. Keep warm over low heat. Serve on toasted buns with pickles and coleslaw, or load into tacos, baked potatoes, or bowls.