Slather the hot dogs with the duck butter or yellow mustard and season all over with the Sweet Rub.
Place the hot dogs directly on the grill grates, close the lid, and smoke for 1 hour.
Remove the hot dogs and slice into 1.5 inch pieces. Place the hot dog pieces into a disposable baking pan. Top with the butter, brown sugar, and BBQ sauce.
Increase the heat on your smoker to 375-400 degrees F or move to the grill. Place the pan of hot dog burnt ends on the grill and cook for an additional 15-30 minutes, stirring regularly, until the butter is melted and the sugars have started to caramelize on the hot dogs.