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 the 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 the 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 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 the mayonnaise, apple cider vinegar, salt, and pepper until evenly coated. Cover and chill until assembly.
07 - Remove the lamb from the oven and shred the meat directly in the pot using two forks, mixing it with the accumulated cooking juices. Drizzle with a generous amount of the Alabama White Sauce and toss to coat evenly.
08 - Layer the sauced pulled lamb onto the bottom half of each slider bun. Top with the prepared slaw and pickled red onions if desired. Drizzle with additional white sauce, cap with the top bun, and serve immediately.