01 - Preheat the oven to 300°F.
02 - In a small bowl, combine the smoked paprika, garlic powder, cumin, salt, and 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 deeply browned, approximately 3 to 4 minutes per side.
04 - Pour the stock into the pot around the lamb. Cover tightly with the lid and transfer to the preheated oven. Roast for 3 hours or until the lamb is fork-tender and shreds apart easily.
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. Cover and refrigerate until ready to use.
06 - In a separate bowl, toss the shredded cabbage and carrot with mayonnaise, apple cider vinegar, salt, and pepper until evenly coated. Cover and refrigerate to allow the flavors to meld.
07 - Remove the lamb from the oven and transfer it to a cutting board. Shred the meat using two forks, discarding any large pieces of fat. Return the shredded lamb to the pot and toss with the accumulated juices. Drizzle with Alabama White Sauce and mix until well coated.
08 - Layer a generous portion of pulled lamb onto the bottom half of each slider bun. Top with slaw and pickled red onions if desired. Drizzle with additional white sauce and cap with the top bun. Serve immediately.