Peel and wash the potatoes and celeriac. Roughly dice both. Peel, core and chop apples.
Cook everything in salted water for about 25 minutes. Roast walnut kernels in hot butter. Heat milk and butter. Drain vegetables. Add butter-milk mixture and crush everything finely. Season to taste with salt and nutmeg.
Serve with nut butter. Goes well with roasted duck breast or game dishes.