Preheat the oven to 400 degrees F. Line a baking sheet with foil.
Scrub the sweet potatoes. Slice each one thinly, stopping about three-quarters of the way through. Place on the lined baking sheet.
Whisk together the melted butter, brown sugar, cinnamon, ginger, nutmeg and salt in a bowl. Pour the mixture over the sweet potatoes very thoroughly. Sprinkle with kosher salt. Cover with foil and bake for 40 minutes.
When ready to serve, put 2 marshmallows on a stick or metal skewer and hold it over an open flame until roasted, slightly charred and golden brown (see Cook's Note). Top a sweet potato with the roasted marshmallows. Repeat with the remaining marshmallows and sweet potatoes.
If you are not by a campfire, you can place the marshmallows on the sweet potatoes and broil on high for 2 to 3 minutes!