Start by applying mustard over the entire chuck roast for the binder. Next season on all side with an all purpose rub.
Preheat the grill to 250 degrees Fahrenheit and set for indirect heat.
Place the seasoned chuck roast directly on the grates and smoke for 3 hours.
Next, transfer the smoked beef into a dutch oven and add all the braise ingredients.
Place the dutch oven on the grill for another 3-4 hours or until the chuck roast is fork tender.
When it's ready, remove the dutch oven from the smoker and let it rest for 20-30 minutes.
Using 2 forks or your hands with heat resistant gloves, shred the chuck roast and mix with the jus in the dutch oven.
Fill the mini french rolls with a handful of the shredded beef, top with a spoonful or more of Giardiniera and enjoy!
