Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish.
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 granulated sugar, brown sugar, milk, melted butter, eggs, vanilla extract, cinnamon, nutmeg, and salt to the mashed sweet potatoes. Mix until well combined and smooth.
Pour the sweet potato mixture into the prepared baking dish and spread it evenly.
Bake in the preheated oven for 25 minutes.
Remove the casserole from the oven and sprinkle the 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.