Buy fennel bulbs with the feathery stalks attached. I buy an extra fennel plant and make stock the night before with the fennel as the predominant aromatic in the stockpot.
In a saucepan, sauté the fennel and leek in the butter over medium heat until the leek is transparent, about 10 minutes. Add the stock, potatoes, and salt. Simmer, uncovered, until all the vegetables are tender, about 45 minutes.
Put the fennel leaves in a food processor and finely chop, then add the soup in batches and puree it. Correct the seasoning and add some cream if desired. Chill, then serve in chilled bowls with a garnish of more fennel leaves, fresh dill, or chives.
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