Break off tough ends of asparagus as far down as stalk snaps easily; discard. Wash thoroughly. Remove scales if sandy or tough; cut stalks into 1-inch lengths. Blanch reserved asparagus tips in boiling salted water until crisp tender, about 1 minute; drain and place on paper towel. Melt butter in heavy 4-quart Dutch oven over medium heat; saute shallots and garlic until tender. Add boiling water, chicken base, asparagus, and potato; bring to a boil. Reduce heat, cover and simmer until potato cubes are tender, about 15 minutes; add chopped chives. Puree (1 1/2 cups) vegetable mixture in blender and transfer into large bowl; repeat 3 times. Stir in buttermilk, salt and white pepper. Allow soup to cool, uncovered, at room temperature for 1 hour; cover and refrigerate until chilled (4-6 hours) or overnight. Transfer soup to tureen or ice bowl. Cut asparagus tips into fine threads and use to garnish top of soup.