Combine the potatoes, celery root, parsnip and bay leaf in a large saucepan and cover with cold water by 1 inch. Season generously with salt and bring to a boil. Reduce the heat to medium and simmer until the vegetables are very tender, about 15 minutes.
Drain the vegetables and discard the bay leaf. Transfer to a food processor, add the butter and puree, gradually adding the milk, until smooth. Season with salt and pepper. Transfer to a serving dish and sprinkle with nutmeg.