2 teaspoons olive oil
The soup can be made up to 1 day ahead, cooled, covered, and refrigerated. Rewarm the soup, covered, over medium-low heat, adding water or milk to thin the soup to the desired consistency, as needed.
Heat a large heavy saucepan over medium-high heat. Add the oil and onion and sauté for about 3 minutes, or until tender. Add the garlic and celery root and cook for about 3 minutes, or until the celery root begins to soften but does not take on any color. Add the stock and the cream and simmer gently for about 15 minutes, or until the celery root is tender.
In a blender, working in batches, puree the celery root and onion mixture with enough liquid to form a smooth soup consistency. Season the soup to taste with salt and pepper.
Ladle the soup into bowls. Garnish with chives and extra-virgin olive oil and serve.