Preheat the smoker to 225-250 F. Set it for indirect heat and add preferred wood chunks.
Start by trimming and large pieces of fat off the sides of the chuck roast and remove any silver skin.
Add a light coating of the mustard binder to the top bottom and all sides of the roast in a thin layer.
Make your own dry rub or use a store bought rub and lightly coat the entire roast on all sides with the rub. Pat it to adhere and set the roast aside for 30 minutes (or prep the night before and leave uncovered in the fridge).
Place the chuck roast on the smoker and insert a meat thermometer into the center of the roast. Allow the chuck roast to smoke for about 1-1.5 hours. Lightly spray the outside of the roast with the beef broth to encourage more smoke adherence to the meat in the beginning of the smoking process.
Repeat this step every hour until the roast reaches and internal temperature of around 165 F. to help build the bark.
Remove the chuck roast from the smoker and place it into a foil wrapping with sliced pads of butter (butter under and on top of the roast) and a few sprays of the beef broth. Wrap it tightly in the foil and place the chuck roast back onto the smoker.
The chuck roast is done when a thermometer probe is inserted to various parts of the meat and the texture feels like softened butter. Alternatively, you can check the temperature of the meat starting around 195 F-203 F.
Remove the chuck roast from the smoker and leave it wrapped in the foil. Wrap it in a towel and place in a cooler to rest for at least and hour before shredding to ensure perfectly shreddable beef.
After resting, shred the chuck roast into pulled beef, discarding any large pieces of fat that didn't bread down during the cooking process. Serve the shredded beef on its own or with BBQ sauce and enjoy!
Notes
If you prefer the bark to be "tighter" in texture, leave the top of the chuck roast exposed and not covered in foil during the wrapping process. This will give more texture to the bark but may make the cooking time longer as a result.