Preheat your oven to 350°F (175°C).
Prepare the sweet potatoes: wash, peel, and chop them into even chunks.
Boil the sweet potatoes in salted water until tender, about 15 minutes.
Drain the sweet potatoes, then mash them in a large bowl.
Mix in melted butter, brown sugar, milk, vanilla extract, and salt.
Transfer the sweet potato mixture into a greased baking dish.
Bake the sweet potato casserole for 25-30 minutes, uncovered.
Remove the casserole from the oven and top with mini marshmallows.
Return to the oven and bake for an additional 10-15 minutes until marshmallows are golden brown.
Let the casserole cool slightly before serving.