Peel the Jerusalem artichokes and place in cold water with a squeeze of lemon until needed (this stops them turning brown). Peel the potatoes, and place into water with artichokes.
In a large pan, heat the butter and oil, and saute the chopped onion and celery until softened but not browned. Remove from the heat for a moment.
Chop the Jerusalem artichokes and potatoes into rough chunks. Return the pan to the heat, and add the Jerusalem artichokes and potatoes. Saute for 2 to 3 minutes, then add the stock and cover the pan with a lid. Ensure the heat is on a low simmer, and leave the soup to cook until vegetables are soft, 30 to 40 minutes. During the cooking time, keep an eye on the liquid levels, and add boiling water if needed.
Blend the soup until it is smooth and creamy with a stick blender or liquidizer.
You may wish to add more stock to lighten it a little, or add cream to enrich it.