Melt the butter in a heavy saucepan. When it foams, add the potatoes and onions and toss them in the butter until well coated.
Sprinkle with salt and a few grinds of pepper. Cover with a butter wrapper or paper lid and the lid of the saucepan. Sweat on a gentle heat for approximately 10 minutes.
Meanwhile, bring the stock to the boil. When the vegetables are soft but not coloured add the boiling stock and continue to cook for about 10-15 minutes or until the vegetables are soft.
Add the milk and purée the soup in a blender or food processor. Taste and adjust seasoning.
Serve sprinkled with a few freshly chopped herbs or some of the following garnishes.