In a saucepan, heat the milk on the stovetop. In the meantime, mash the boiled, peeled potatoes using a potato masher. If you prefer a smoother puree, mash a second time.
Put the mashed potatoes in a pot on the stove and stir while adding the milk. Then add pepper, butter, salt and nutmeg and continue stirring. If you want to make the puree softer, add a little bit of water.
Finally add the Parmigiano-Reggiano and remove any lumps by stirring with a whisk. The puree is ready to be served when smooth, plump and uniform in consistency.