Peel the potatoes, leek, and onion; wash them. Cut the vegetables into small pieces.
Place the vegetables and water in a large pot; season with salt and pepper. Bring to a boil; cover and simmer for 1 hour.
Once the soup is done cooking, purée it in a food mill or blender; return the soup to the heat.
Warm a soup tureen; heat the milk in a small saucepan. Pour the warm milk into the soup tureen; add the butter; stir.
Pour the boiling soup over the milk and butter mixture.
If you have chervil on hand when making this soup, you can finely chop a few sprigs and sprinkle them over the soup just before serving: it will taste even better.