Boil and mash the potatoes.
Make a roux of the butter, flour, and onion, letting the onion cook in the butter a few minutes before adding the flour. When the roux is cooked add to it the milk, making a thin, white sauce. Add this to the mashed potato and pass the whole through a strainer. Return it to the fire for a few minutes to heat and blend it. Season it with salt and pepper.
Sprinkle on the soup, when it is in the tureen, the parsley and a few croutons.
If the soup is too thick, add a little more milk or a little hot water. The roux prevents the milk and potato from separating, and also gives it smoothness. The soup can be made richer by using more milk, and stirring into it, just before serving, the beaten yolks of two eggs. This soup may also be made of sweet potatoes.