Heat your grill or smoker to 275℉ with your choice of wood or pellets.
Rub about 1 tablespoon of Worcestershire sauce over the entire roast to use as a binder. Then season all sides of your beef roast liberally with your favorite barbecue seasoning. *See notes on seasoning.
Place the chuck roast directly on the grill grates and smoke at 275℉ until the roast reaches an internal temperature of about 165℉. *This could take about 3-5 hours, depending on the size of your roast and the heating capabilities of your grill.
Once the roast reaches 165℉, take it off the grill and make the braising liquid. Add beef stock, BBQ sauce, Worcestershire sauce, and optional apple cider vinegar to the bottom of a half-size foil pan and whisk it together. Then place the smoked chuck roast in the pan, turning it over a few times to coat the beef in the liquid. Cover the pan tightly with aluminum foil.
Put the foil pan on the grill, and braise the roast at 275℉ until it reaches an internal temp of about 195℉ - about 1½ to 2 hours, but cooking times will vary.
Transfer the beef to a cutting board to rest for about 15-20 minutes. Pour the braising liquid into a separate container to save for later.
Cut the rested chuck roast into cubes about 1" in size. Add the chuck roast cubes back to the foil pan, and toss with about ⅓ cup of barbecue sauce. Sprinkle with about ½ to 1 tablespoon of barbecue seasoning. Pour about ¼ cup of the reserved braising liquid into the bottom of the pan to prevent the beef nuggets from sticking and to keep them moist.
Place the foil roasting pan on the grill, and cook uncovered for about 1½ hours, or until the burnt ends are very tender and the sauce has tacked up to a nice glaze consistency.
Remove the burnt ends from the grill, toss in the pan sauce, and let them rest for about 10 minutes before serving.