01 - Preheat the oven to 300°F. In a small bowl, combine smoked paprika, garlic powder, cumin, kosher salt, and black pepper. Rub the spice mixture evenly over the entire surface of the lamb shoulder, pressing gently to adhere.
02 - Heat olive oil in a large Dutch oven or ovenproof pot over medium-high heat. Sear the lamb shoulder on all sides until deeply browned, approximately 3 to 4 minutes per side.
03 - Pour the stock into the pot around the lamb. Cover tightly with a lid and transfer to the preheated oven. Roast for 3 hours or until the lamb is fork-tender and pulls apart with minimal effort.
04 - While the lamb braises, whisk together mayonnaise, apple cider vinegar, prepared horseradish, Dijon mustard, lemon juice, garlic powder, onion powder, black pepper, and salt in a mixing bowl until smooth. Refrigerate until ready to use.
05 - Toss shredded cabbage and carrot with mayonnaise, apple cider vinegar, salt, and pepper in a bowl until evenly coated. Chill until serving.
06 - Remove the lamb from the oven and shred it directly in the pot using two forks, mixing the meat with the accumulated juices. Drizzle with Alabama White Sauce and toss to coat evenly.
07 - Layer the sauced pulled lamb onto the bottom half of each slider bun. Top with crisp slaw and pickled red onions if desired. Drizzle with additional white sauce and cap with the top bun. Serve immediately.