Heat the butter in a soup pot over medium-high heat and cook the onions, celery, and mushrooms. Add the garlic and sauté for 1 minute. Sprinkle with salt.
Add the jerusalem artichokes and the vegetable stock to the pot and bring to a simmer. Reduce the heat to low, and simmer, covered, until the jerusalem artichokes begin to break down, 45 minutes to an hour.
Using an immersion blender or upright blender, purée the soup. Add salt to taste.