Heat the oven to 350°F.

Place the sweet potatoes in a large pot and add enough cold water to cover by about 1 inch. Bring to a boil over high heat. Reduce the heat to maintain a simmer and cook until fork-tender, about 12 to 15 minutes.

Drain the potatoes, then return to the pot. Add the brown sugar, whole milk, melted butter, vanilla extract, and kosher salt. Mash with a potato masher until smooth.

Transfer the mixture to a 9x13-inch baking dish and spread into an even layer. Arrange the marshmallows evenly over the top in a single layer.

Bake until the sweet potatoes are heated through and the marshmallows are golden-brown and puffed, about 18 to 20 minutes.