Peel and cube the sweet potatoes, then boil in a large pot of water for 15-20 minutes until tender. Drain and cool slightly.
Mash the sweet potatoes in a mixing bowl until smooth. Add granulated sugar, brown sugar, milk, melted butter, vanilla extract, ground cinnamon, ground nutmeg, and salt. Mix until creamy.
Measure out 2 cups of mini marshmallows and set aside.
Transfer the sweet potato mixture to a greased 9x13-inch baking dish. Spread evenly and top with mini marshmallows.
Preheat oven to 350°F. Bake for 25 minutes, then check. If the sweet potato base is warm, return to oven for an additional 10-15 minutes until marshmallows are golden brown.
Let cool for a few minutes before serving.