Preheat smoker or grill for 275 degrees F.
Wash and gently scrub sweet potatoes under lukewarm water—dry well with paper towels.
Lightly puncture the peels with a fork. Coat each potato will oil and salt.
Place sweet potatoes into your grill or smoker, close the lid, and cook for 1 1/2-2 hours, or until they are fork-tender.
Remove potatoes from the grill and place them onto a large cutting board. Increase the heat of your grill or smoker to 475 degrees F.
Combine softened butter with brown sugar, cinnamon, ginger, and nutmeg.
Slit each sweet potato down the center lengthwise. Avoid cutting them all the way through. Use the above picture as a guide.
Scoop equal portions of butter mixture into each sweet potato, and top with 1/4 cup of mini marshmallows.
Arrange sweet potatoes into a large smoker safe pan, marshmallow side up.
Once your smoker (or grill) has reached 475 degrees F, place the pan with the sweet potatoes on the grill grates. Close the lid and broil them for 3-5 minutes, or until the marshmallows have browned and softened.
You can also broil the smoked sweet potatoes using your oven.
Remove your smoked loaded sweet potatoes from the smoker and let them stand for 10 minutes before serving.
Store leftovers in an airtight container in the refrigerator for 3 days. Rewarm in a 350-degree oven. See notes for oven method!