In a small saucepot, place potatoes and cover with cold water. Place over high heat and bring up to a bubble. Cook until tender, about 15 minutes.
In another small saucepot, add parsnips, celeriac and milk, and bring up to a bubble. Cook until tender, about 20 minutes.
When everybody is tender, scoop a mug of hot milk out of the parsnips and celeriac, then drain and smash potatoes, parsnips, and celeriac together along with nutmeg, butter, reserved hot milk, salt and ground black pepper.