Preheat your oven to 350°F (175°C).
In a large pot, bring water to a boil. Add the cubed sweet potatoes and cook until tender, about 15-20 minutes. Drain and let cool slightly.
In a large mixing bowl, mash the sweet potatoes until smooth.
Add brown sugar, softened butter, milk, vanilla extract, cinnamon, nutmeg, and salt to the mashed sweet potatoes. Mix until well combined and creamy.
Transfer the sweet potato mixture to a greased 9x13-inch baking dish, spreading it evenly.
Bake in the preheated oven for 25 minutes.
Remove from the oven and sprinkle mini marshmallows evenly over the top.
Return to the oven and bake for an additional 10-15 minutes, or until the marshmallows are golden brown and toasted.
Allow to cool for a few minutes before serving.