Preheat your smoker to 225 F
Slather your hot dogs with mustard and then sprinkle on the barbecue rub
Place the hot dogs on the smoker and let them smoke for about an hour
Remove the hot dogs and slice them into pieces about 1 to 1.5 inch pieces. Place the hot dog pieces in a disposable aluminum pan and top with the butter, brown sugar, and barbecue sauce. Mix well to coat the hot dogs
Finish them off by placing back on your smoker or on a grill at a higher temperature (350 F to 375 F) and cooking for another 15 to 30 minutes, stirring occasionally
When the sauce has come together and started to thicken and caramelize, remove the hot dog burnet ends from the smoker, transfer to a serving bowl, and serve while warm