For the cream of mushroom soup, melt half the butter in a large saucepan and sauté the onion over low heat for 10 minutes until translucent. Add the remaining butter and mushrooms and saute for another 5 minutes, until the mushrooms are browning. Add broth and tarragon and bring to a boil, then reduce heat and simmer gently for 20 minutes.
Puree with a hand blender until smooth. Stir in the creme fraiche and season to taste with salt and pepper. Slowly reheat the soup. Serve the cream of mushroom soup with chopped tarragon.