Preheat the oven to 350°F (175°C).
Prepare the potatoes by peeling and cubing them, then place them in a large pot of salted boiling water.
Drain the potatoes and return them to the pot. Add heavy cream, melted butter, brown sugar, and vanilla extract.
Use a potato masher or mixer to mash the mixture until smooth and well combined.
Spread the potato mixture evenly in a greased baking dish.
Top the casserole with mini marshmallows, spreading them evenly.
Bake in the preheated oven for 30-35 minutes, until the marshmallows are golden brown.
Remove from the oven and let it cool slightly before serving.