Remove leaves and core from the cauliflower, divide into florets and put in a large pot. Peel the potato and onion and cut into dice, add to the cauliflower together with butter and half the oil. Heat over low heat until vegetables start to sizzle. Cover and heat for another 10 minutes, stirring occasionally, until vegetables soften but do not brown.
Pour in stock, bring to a boil, add milk and bring to a boil again over low heat. Season with salt and pepper, cook over low heat uncovered for 10-15 minutes until vegetables are completely soft.
Remove from heat and add cream, blend the soup. Press the soup through a strainer with a wooden spoon to achieve a perfect cream. Before serving, heat the soup well but do not boil.
Wash and dry the chanterelles thoroughly, cut into smaller pieces. Heat the remaining oil in a pan and fry the mushrooms until lightly browned. At the end season with salt and pepper.
Pour soup into bowls, add chanterelles and sprinkle with chives. Can be served with croutons. Instead of in the soup, the chanterelles can be placed on croutons.