Preheat oven to 350°F and grease a 9x13 inch baking dish.
Boil sweet potatoes in a large pot of water until fork-tender, about 15-20 minutes, then drain well.
Mash the sweet potatoes until smooth, then mix in melted butter, milk, sugar, beaten eggs, vanilla, cinnamon, nutmeg, and salt until well combined and creamy.
Spread the sweet potato mixture evenly into the prepared baking dish.
Bake uncovered for 25 minutes until heated through and set.
Remove from oven and top evenly with mini marshmallows, then return to oven for 5-7 minutes until marshmallows are golden brown.
Let cool for 5 minutes before serving.