Peel and dice the potatoes and cook as usual. Then roughly (!) Tamp - you should still see large lumps in it. Now pour the milk over it (the consistency is then something like a thick pea soup). Bring to the boil briefly, then add the butter and stir in.
Arrange and serve on plates.
Cut the sausage into cubes and serve with it - everyone can then sprinkle them on the milk potatoes to their liking.