Melt the butter in a large, heavy-based saucepan set over a medium heat. Sweat the shallot and leek for 8-10 minutes, stirring occasionally, until they soften and turn translucent in appearance.
Add the potato, stock and bay leaf and bring to a simmer. Cook at a simmer for 10-15 minutes until the potato is tender. Remove and discard the bay leaf, then puree the soup using a stick blender until smooth. Add the milk and puree again. Season to taste.
Allow to cool to room temperature, then cover and chill until needed. Serve chilled in soup bowls with a sprinkle of chives on top.
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