In a large pot, combine the butter and olive oil. Heat on medium until the butter is melted.
Add the diced celeriac, potato and onion to the pot. Cook, stirring occasionally until the celeriac begins to brown, about 10 minutes.
Add the broth and allow to cook for about 15 minutes, or until the potatoes are soft.
Use an immersion blender to puree the soup completely. (If you don’t have an immersion blender, use a regular blender to puree the soup a few cups at a time). Stir in the dried tarragon.
Serve and enjoy!