Trim the leeks by removing outer leaves. Cut off the roots and cut off where the leaves start to spread. Wash leeks well between the leaves in case of sand and dirt. Slice thinly.
In a large soup pot (5 or 6 cup pot) sauté the leeks and potatoes in the butter until tender. Add half the stock to the pot. Using a hand held immersion blender, finely blend the vegetables until smooth. Add the rest of the stock, cream, salt and pepper.
Simmer for 20 minutes, serve garnished with chives.
This recipe is also known as Vichyssoise which is served cold.