Prepare the smoker for barbecuing, bringing the temperature to 200°F to 220°F.
In a cast-iron skillet or smoke-proof baking dish, melt the butter. Stir in the sweet potatoes and then pat the potatoes down into a thick, even layer. Sprinkle the brown sugar and the salt over the potatoes.
Transfer the potatoes to the smoker and cook for 1 hour. Stir in