Bake the sweet potatoes: Place unpeeled sweet potatoes on a baking sheet and baking in a 400 degree F oven for about one hour. (Tip: Place a piece of aluminum foil on the baking sheet for easy cleanup!)
Once the potatoes are cooked, slice in half and scoop out the flesh.
In a mixing bowl, combine the cooked sweet potato, brown sugar, salt, vanilla, eggs, and melted butter. Mix until well blended.
Transfer filling to a greased 2 quart baking dish.
Bake in a 350 degree F oven for 30 minutes. Remove from the oven and sprinkle with mini marshmallows over the top.
Return to the oven for 10 minutes, or until the marshmallows are lightly browned.