Preheat your oven to 350°F and lightly grease a baking dish. Drain the canned sweet potatoes and add them to a large mixing bowl.
Mash the sweet potatoes until smooth. Stir in melted butter, brown sugar, milk, vanilla, cinnamon, and nutmeg until fully combined.
Spread the sweet potato mixture evenly into the prepared baking dish. Smooth out the top with a spatula.
Sprinkle mini marshmallows over the top in an even layer. Bake for 25–30 minutes until the casserole is hot and the marshmallows are puffed and golden brown.