How to Make It
In a saucepan of boiling salted water, blanch the asparagus tips until crisp-tender, about 1 minute. Drain the asparagus tips in a colander and refresh under cold water. Pat dry, halve the tips lengthwise and set aside.
Melt the butter in a large saucepan.Add the leeks and cook over moderate heat, stirring, until softened, about 5 minutes. Add the asparagus stalks, potatoes, stock, water and thyme and bring to a boil. Reduce the heat to low, cover and simmer until the potatoes are tender, about 15 minutes.
Discard the thyme sprig. Working in batches, puree the soup in a blender, then transfer to a large bowl. Stir in the milk, salt and white pepper. Let the soup cool to room temperature, then refrigerate until chilled, at least 4 hours or overnight.
Ladle the soup into chilled bowls and drizzle with Chive Oil. Garnish with the asparagus tips and serve.