Prepare a smoker or charcoal grill for indirect cooking at 225 degrees F.
Slather the hot dogs with the yellow mustard and sprinkle all over with the rub. Add wood to the smoker or grill, then 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 1/2-inch pieces. Increase the heat on your smoker or grill to 375 to 400 degrees F. Place the hot dog pieces in a disposable baking pan. Top with the butter, brown sugar and barbecue sauce. Place the pan of hot dog burnt ends on the grill grates and cook, stirring regularly, until the butter is melted and the sugars have started to caramelize on the hot dogs, an additional 15 to 30 minutes. Serve and enjoy!
These Hot Dog Burnt Ends exist because sometimes you wanna barbecue, but you still need to watch your budget. Sweet, smoky, and full of flavor, these morsels will be a huge hit at your next party!