Melt butter in a soup pot over medium heat and cook onion for 7 minutes until soft. Add celery root and cook for 3 minutes, stirring.
Add potatoes, broth, bay leaf, salt and white pepper. Bring to a simmer, cover partly and cook for 20 to 25 minutes until both vegetables are tender.
Remove the bay leaf. Mash directly in the pot with 6 to 8 firm strokes of a potato masher, leaving most potato cubes intact.
Stir in milk and cream. Warm over low heat for 5 minutes until steaming, stirring along the bottom and avoiding a hard boil.
Divide among 6 bowls, spooning both the creamy broth and the potato pieces into each portion.