Boil the sweet potatoes: Place the cubed sweet potatoes in a large pot of salted water. Bring to a boil and cook until a fork slides in easily, about 15-20 minutes, then drain well.

Mash with butter and sugar: While the sweet potatoes are still hot, mash them with the butter and brown sugar until smooth. Working while hot prevents the mash from turning gluey.

Mix in the wet ingredients: Whisk in the eggs, milk and vanilla extract until fully combined. Stir in the cinnamon, nutmeg and salt.

Preheat the oven: Preheat your oven to 350°F. Grease a 9x13 inch baking dish with butter or oil.

Spread the filling: Transfer the sweet potato mixture into the prepared dish and smooth the top evenly with a spatula.

Bake the base: Bake for 25 minutes, until the edges start to bubble gently and the center feels set when lightly pressed.

Add the marshmallows: Remove the dish from the oven and scatter the marshmallows evenly over the top in a single layer.

Bake until golden: Return the dish to the oven and bake for 8-10 minutes, until the marshmallows puff up and start to brown at the edges.

Broil for color: If you want deeper browning, broil for 1-2 minutes, watching constantly since marshmallows darken fast.

Rest before serving: Let the casserole sit for 5 minutes so the filling sets slightly before scooping and serving warm.