Once the grill or smoker is near its temperature, add your wood chips, wood chunks, or pellets into a pellet tube smoker and place over the direct heat and close the lid.
Once the grill or smoker is up to 325°F and producing smoke, place the entire baking tray with the sweet potatoes into the smoker, or on the cool side of the grill.
Every 30 minutes, baste the smoked sweet potatoes with more softened butter, sugar, and rub. You can also baste the melted butter that has collected at the bottom of the pan. Make sure to get in between each slice. Then close the lid again. Smoke for about 2 hours total.
Check for doneness by piercing the potato with a knife or fork. It should pass through effortlessly when they are finished. Or you can use an instant read thermometer and look for an internal temperature of 200-210*F.
Remove the tray from the grill or smoker using oven safe BBQ gloves and place somewhere to cool for 10-15 minutes before serving. Sprinkle with more dark brown sugar once cooled if you wish.