01 - Preheat 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 shreds apart with minimal effort.
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. Cover and refrigerate until ready to use.
06 - In a separate bowl, toss shredded cabbage and carrot with mayonnaise, apple cider vinegar, salt, and pepper until evenly coated. Cover and refrigerate to allow flavors to meld.
07 - Remove the lamb from the oven and transfer to a cutting board. Shred the meat using two forks, discarding any large pieces of fat. Return the shredded lamb to the pot with the cooking juices. Drizzle with Alabama White Sauce and toss to coat evenly.
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.