- Melt butter in heavy large pot over medium heat.
- Add leaks and garlic; saute until tender, about 6 minutes
- Add potatoes and zucchini; saute for 5 minutes
- Add 4 1/2 cups broth and bring to a boil.
- Reduce heat and simmer until potatoes are tender, about 15 minutes.
- Cool for 30 minutes.
- Working in batches, puree soup in blender, or use a hand blender.
- Mix in half and half.
- Season to taste with salt and pepper.
- Cover and refrigerate until cold, about 4 hours. (Can be made a day ahead. Keep refrigerated.)
- Sprinkle with chives and serve.