3 tablespoons unsalted butter
1 large leek, white and light green parts only, thinly sliced
1 medium onion, chopped
1 small fennel bulb—halved, cored and chopped
1 medium celery rib, thinly sliced
1 medium shallot, finely chopped
1 thyme sprig
1 large garlic clove, minced
Salt 8 cups chicken stock or low-sodium broth
1 1/2 pounds Yukon Gold potatoes, peeled and cut into 1/2-inch pieces
3 tablespoons finely chopped parsley
2 tablespoons finely chopped tarragon
1 cup heavy cream
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.
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.
The soup can be refrigerated for up to 2 days.