Pat the lamb shoulder dry with paper towels. In a bowl, combine the salt, pepper, garlic powder, smoked paprika, brown sugar, ground cumin, and chopped rosemary.
Rub the dry rub mixture all over the lamb shoulder and let it rest for at least 2 hours, or preferably overnight.
In a large skillet, heat the olive oil over medium-high heat. Sear the lamb shoulder on all sides for 3-4 minutes until golden brown.
Place the seared lamb shoulder in a slow cooker or a Dutch oven. Add the chopped onion, BBQ sauce, Worcestershire sauce, apple cider vinegar, and water/broth.
Cover and cook on low for 7-8 hours (or bake in the oven at 265°F/130°C) until the lamb is completely tender.
Once the lamb is cooked, remove it from the pot and shred it using two forks.
Mix the shredded lamb with the cooking juices and a little extra BBQ sauce. Let it rest for a few minutes to allow the flavors to meld.
Serve on fresh buns, with grilled vegetables, or coleslaw. Garnish with fresh parsley, if desired.
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