Bring the milk with salt and nutmeg to the boil. Stir in the polenta and let it steep for 5 minutes with the stove switched off. Add the egg, parmesan, butter and parsley.
Form small dumplings with two teaspoons and place in boiling salted water. The dumplings are ready when they rise to the surface.
The dumplings taste good in clear soups or in vegetable stews.