01 - In a small bowl, combine smoked paprika, brown sugar, garlic powder, onion powder, black pepper, salt, and cayenne pepper. Mix thoroughly until evenly blended.
02 - 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.
03 - Pour the beef broth and 1 cup of BBQ sauce over the seared roast. Cover tightly with a lid and transfer to an oven preheated to 300°F. Braise for approximately 3 hours, or until the beef is fork-tender and shreds effortlessly.
04 - Remove the beef from the Dutch oven and shred using two forks, pulling the meat apart along its natural grain. Mix the shredded beef with pan juices and additional BBQ sauce to taste.
05 - In a small bowl, whisk together mayonnaise, apple cider vinegar, Dijon mustard, honey, salt, and pepper until smooth and well combined.
06 - In a large bowl, combine the shredded green cabbage, red cabbage, carrots, and sliced red onion. Pour the dressing over the vegetables and toss until evenly coated. Refrigerate until ready to serve.
07 - Lightly toast the sandwich buns if desired. Pile a generous portion of shredded BBQ beef onto the bottom half of each bun. Top with a hearty scoop of crunchy coleslaw, drizzle with extra BBQ sauce if desired, and cap with the top bun. Serve immediately.