01 - Preheat oven to 300°F. In a small bowl, combine smoked paprika, brown sugar, garlic powder, onion powder, black pepper, salt, and cayenne pepper. Rub the spice mixture evenly over the entire surface of the beef chuck roast. Heat olive oil in a large Dutch oven over medium-high heat. Sear the beef on all sides until deeply browned, approximately 8 minutes total.
02 - Pour the beef broth and 1 cup of BBQ sauce over the seared beef. Cover the Dutch oven tightly with its lid and transfer to the preheated oven. Roast for approximately 3 hours, or until the beef is fork-tender and shreds apart effortlessly.
03 - Remove the Dutch oven from the oven and transfer the beef to a cutting board. Using two forks, shred the meat, discarding any large pieces of fat. Return the shredded beef to the pot and toss with the pan juices. Add extra BBQ sauce to taste and keep warm.
04 - In a small bowl, whisk together the mayonnaise, apple cider vinegar, Dijon mustard, honey, salt, and pepper until smooth and well combined.
05 - In a large mixing bowl, combine the shredded green cabbage, red cabbage, carrots, and sliced red onion. Pour the dressing over the vegetables and toss thoroughly until everything is evenly coated. Refrigerate until ready to serve.
06 - Lightly toast the sandwich buns if desired. Mound a generous portion of shredded BBQ beef onto the bottom half of each bun. Top with a heap of crunchy coleslaw, drizzle with additional BBQ sauce if desired, and cap with the top bun. Serve immediately.