Peel and chop the sweet potatoes into large chunks, placing them in a pot of boiling salted water. Cook for 15 to 20 minutes, or until fork-tender. Drain the potatoes and transfer them to a large mixing bowl, mashing them until smooth and creamy.

In the bowl with the mashed sweet potatoes, mix in melted butter, light brown sugar, vanilla extract, cinnamon, salt, and nutmeg. Stir until all ingredients are well combined.

While the filling cools slightly, preheat your oven to 350°F (175°C).

Grease a 9x13-inch baking dish with butter. Carefully spread the sweet potato filling evenly across the bottom of the dish.

Place the casserole in the oven and bake for 25 to 35 minutes. Monitor the marshmallows as they puff up and turn golden brown.

After baking, allow the casserole to cool for about 10 minutes before serving.