IMPORTANT: Leeks are known to hold sand. Wash them or soak them well before cooking (see image).
In a large, heavy bottom pot, melt butter over medium-low heat. Once butter is melted, add the leeks and sweat for 5 minutes, making sure they do not take on any color
Add potatoes and cook for a minute or two, stirring a few times.
Stir in the chicken broth and bring to a boil.
Reduce heat to a simmer. Cook on low heat, gently simmering for 35 minutes, or until the leeks and potatoes are very soft. Allow to cool for a few minutes.
Slowly and in SMALL batches, puree the soup at high speed in the blender. Do this bit by bit, never filling the blender too high.
Return soup to the cooking pot and whisk in cream and nutmeg. Season with salt and pepper. Return to a boil, reduce to simmer, and cook 5 minutes. If you want to thin the soup out, add more broth.
Transfer soup to the mixing bowl and chill over the ice bath, stirring occasionally. When the soup is at room temperature, cover in plastic wrap and put into the refrigerator to cool.
Check seasoning, sprinkle with chives and serve in chilled bowls
This soup gets better over time. Enjoy this amazing but easy French treat!