01 - Preheat the oven to 300°F.
02 - 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.
03 - Heat olive oil in a large Dutch oven or ovenproof pot over medium-high heat. Sear the lamb shoulder on all sides until a deep golden-brown crust forms, approximately 3 to 4 minutes per side.
04 - 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 effortlessly.
05 - 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 medium bowl until smooth. Refrigerate until ready to use.
06 - Toss shredded cabbage and carrot with mayonnaise, apple cider vinegar, salt, and pepper in a bowl until evenly coated. Chill until serving time.
07 - Remove the lamb from the oven and shred it directly in the pot using two forks, mixing the meat with the accumulated cooking juices. Drizzle generously with Alabama White Sauce and toss to coat evenly.
08 - Layer a generous portion of 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, cap with the top bun, and serve immediately.