Peel and dice potatoes and in a bowl combine with water. Discard dark green tops of leeks and chop remaining leeks. In another bowl soak leeks in water to cover, agitating occasionally to dislodge any sand, 5 minutes. Lift leeks out of water and drain in a colander.
In a heavy kettle cook leeks and onion in butter over low heat, stirring occasionally, until leeks are softened. Add potatoes with water and salt and simmer, covered, 40 minutes, or until potatoes are very soft. Add milk and half-and-half or cream and bring just to a boil, stirring.
In a blender puree soup with 1/2 cup chilies in batches until smooth, straining as pureed through a very fine sieve into a large bowl, and stir in sour cream and lime juice. Chill soup, covered, until very cold and up to 1 day.
Cut remaining chilies into small dice. Serve soup garnished with lime slices and diced chilies.
recipe courtesy of Gourmet Magazine