Preheat smoker to 250 degrees F. Cover the hot dogs in the yellow mustard and then sprinkle them with Sweet & Smoky Rub making sure to evenly distribute.
Place the hot dogs directly onto the smoker grates of the preheated smoker, close the lid and smoke for 1 hour.
Remove the hot dogs from the smoker and slice them into 1 ½ inch pieces. Place the sliced hot dogs into a disposable pan. Top them with butter, brown sugar and BBQ sauce.
Increase the heat on your smoker to 375 degrees F. Place the pan of hot dogs on the grill and cook for an additional 30 minutes, stirring regularly, until the butter is melted and sugars have started to caramelize on the hot dogs.