Preheat oven to 375 degrees. Place sweet potatoes in a large saucepan, and cover with cold water by 1 inch; salt generously. Bring to a boil; reduce to a simmer, and cook until easily pierced with the tip of a paring knife, 15 to 20 minutes. Drain, and return to pan. Heat over medium, stirring, until liquid has evaporated and a thin film covers bottom of pan, about 2 minutes.
Remove pan from heat; add milk, butter, and nutmeg. Mash until smooth; season with salt and pepper. Transfer sweet-potato mixture to a 2-quart baking dish. (To make ahead, refrigerate, up to 1 day.)
Top casserole with marshmallows; bake until center is warmed through and marshmallows are lightly browned, 15 to 20 minutes.