01 - Preheat the oven to 300°F.
02 - In a small bowl, combine the 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 with minimal effort.
05 - While the lamb braises, whisk together the mayonnaise, apple cider vinegar, prepared horseradish, Dijon mustard, lemon juice, garlic powder, onion powder, black pepper, and salt in a medium bowl until smooth and well combined. Refrigerate until ready to use.
06 - Toss the shredded cabbage and carrot with mayonnaise, apple cider vinegar, salt, and pepper in a bowl until evenly coated. Refrigerate until assembly.
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 with a generous amount of Alabama White Sauce and toss to coat evenly.
08 - Layer the sauced pulled lamb onto the bottom half of each slider bun. Top with a spoonful of slaw and pickled red onions if desired. Drizzle with additional white sauce and cap with the top bun. Serve immediately.