Preheat oven to 350°F. Boil potatoes until fork-tender, about 15–20 minutes.

Drain and mash potatoes with milk, butter, brown sugar, vanilla, and salt until smooth.

Spread mash into a 9x13-inch baking dish and smooth the top.

Bake uncovered 20 minutes, then sprinkle marshmallows evenly over the top.

Return to oven and bake 5–8 minutes more, until marshmallows are golden and puffy. Watch closely.