In a large pot over medium-low heat, melt the butter. Add the leeks and onion and cook, stirring occasionally, until soft but not browned, about 20 minutes.
Add the potatoes, 4 cups water, and salt to taste, and turn up the heat to high to bring it to a boil.
Turn down the heat to medium-low, and continue cooking, stirring occasionally, until the potatoes are soft, 50–60 minutes.
Whisk in the milk and light cream, bring the soup to a boil over high heat, then remove from heat and let cool.
Add cooled soup till a blender with heavy cream.
Refrigerate until chilled, for at least 2 and up to 24 hours. Season soup with salt to taste just before serving. Garnish with chives.
