Step 1

In a large saucepan, melt the butter. Add the leek, onion, fennel, celery, shallot, thyme, garlic and a generous pinch of salt and cook over moderate heat, stirring occasionally, until the vegetables are softened and just starting to brown, about 10 minutes. Add the stock, potatoes, 2 tablespoons of the parsley and 1 tablespoon of the tarragon. Bring to a boil, then simmer over moderately low heat until the vegetables are very tender, about 40 minutes.

Step 2

Add the cream to the saucepan and simmer over moderate heat until slightly thickened, about 7 minutes. Stir in the remaining 1 tablespoon each of parsley and tarragon and season the soup with salt and white pepper; discard the thyme sprig. Ladle the soup into bowls and serve.