Prepare smoker for indirect cooking at 225°F using cherry and oak wood for flavor.

Spread yellow mustard evenly over all surfaces of each hot dog. Sprinkle sweet barbecue rub all over the hot dogs until fully coated.

Place hot dogs directly on smoker grates and smoke for 1 hour, until hot dogs take on a reddish color.

Remove hot dogs from smoker and slice each diagonally into 1 1/2-inch pieces. Place pieces in a disposable foil pan.

Top hot dog pieces with cubed butter, brown sugar, and barbecue sauce. Toss gently to coat.

Increase smoker heat to 375-400°F. Place foil pan on grill grates and cook 15-30 minutes more, stirring occasionally, until butter is melted and sugars are caramelized on edges.

Transfer burnt ends to a platter. Serve immediately while hot, or let cool slightly before serving.