In a saucepan, melt 4 tablespoons of the butter over moderately low heat and in it sauté the onion until soft.
Add the potato, celery roots, bay leaf, and enough stock to cover the vegetables and bring to a boll. Lower the heat and simmer, partially covered, until the vegetables are tender, about 20 minutes.
Remove the bay leaf and purée the vegetables in a food processor or food mill.
Return the purée to the pan. Add the remaining stock and tarragon, bring to a simmer, and add salt and pepper to taste.
In a small bowl, blend the sour cream and heavy cream and beat in egg yolks. Whisk in 1 ladleful of hot soup and whisk this mixture into the soup, stirring constantly. Cook until the soup is heated through. Do not allow the soup to boil or the eggs will curdle.
Remove from heat and stir in the remaining tbsp of butter, softened. Serve in heated bowls and garnish with the chopped celery leaves.