01 - Preheat the oven to 300°F (150°C).
02 - Pat the beef chuck roast dry with paper towels. In a small bowl, combine olive oil, kosher salt, freshly ground black pepper, smoked paprika, garlic powder, onion powder, and ground cumin. Rub this mixture evenly over all surfaces of the beef.
03 - Heat a large Dutch oven or oven-safe pot over medium-high heat. Once hot, carefully sear the seasoned beef roast on all sides until a rich, golden-brown crust forms, approximately 2-3 minutes per side.
04 - Pour the beef broth, 1 cup of barbecue sauce, apple cider vinegar, and Worcestershire sauce into the pot. Bring the liquid to a gentle simmer, scraping up any browned bits from the bottom of the pot.
05 - Cover the Dutch oven tightly and transfer it to the preheated oven. Braise the beef for 4 hours, or until it is exceptionally tender and can be easily shredded with a fork.
06 - While the beef braises, prepare the coleslaw. In a medium mixing bowl, combine the shredded green cabbage, shredded carrots, mayonnaise, 1 tablespoon apple cider vinegar, and granulated sugar. Stir well to combine. Season with salt and freshly ground black pepper to taste. Chill in the refrigerator until ready to serve.
07 - Carefully remove the Dutch oven from the oven. Using two forks, shred the tender beef directly in the pot, ensuring it mixes thoroughly with the flavorful cooking juices.
08 - If desired, lightly toast the soft sandwich buns or brioche rolls.
09 - To assemble, place a generous portion of the shredded pulled beef onto the bottom half of each toasted bun. Top with a spoonful of the prepared coleslaw, a drizzle of extra barbecue sauce, and dill pickle slices, if using. Place the top bun and serve the sandwiches hot.