Peel and cube the sweet potatoes into 1-inch pieces. Place them in a large pot, cover with water, and bring to a boil. Cook for 15-20 minutes until fork-tender, then drain well.
Preheat your oven to 350°F and grease a 9x13-inch baking dish.
In a large bowl, mash the sweet potatoes until smooth (a hand mixer works great for this!).
Add the melted butter, both sugars, milk, beaten eggs, vanilla, cinnamon, and salt. Mix until everything is well combined and creamy.
Pour the sweet potato mixture into your prepared baking dish and smooth the top.
Bake for 25 minutes, then remove from the oven and cover the entire top with mini marshmallows.
Return to the oven and bake for an additional 5-10 minutes, watching carefully, until the marshmallows are golden brown and perfectly toasted. Serve warm!