01 - Preheat oven to 300°F. Combine brown sugar, smoked paprika, kosher salt, black pepper, garlic powder, onion powder, and cayenne pepper in a small bowl. Pat beef chuck roast dry and coat thoroughly with the spice mixture.
02 - Place seasoned beef in a large Dutch oven or roasting pan. Pour beef broth, apple cider vinegar, Worcestershire sauce, and Dijon mustard around the meat, avoiding direct rinsing of the spice rub.
03 - Cover container tightly with lid or aluminum foil. Roast for 4 to 4½ hours until beef reaches fork-tender consistency and shreds effortlessly.
04 - While beef roasts, combine ketchup, apple cider vinegar, brown sugar, molasses, Worcestershire sauce, smoked paprika, garlic powder, and onion powder in a saucepan. Simmer over medium-low heat for 15 minutes, stirring occasionally. Season with salt and pepper to taste.
05 - Transfer cooked beef to a large bowl. Using two forks, shred meat while discarding excess fat pieces.
06 - Skim fat from braising liquid. Add ½ cup of defatted liquid to shredded beef for moisture. Fold in half of the prepared BBQ sauce, reserving the remainder for serving.
07 - Lightly toast sandwich buns if desired. Pile sauced beef onto buns, top with coleslaw and pickles. Drizzle additional BBQ sauce over the top as preferred.
08 - Serve sandwiches immediately while beef is warm and buns maintain texture.