The ingredients as listed here would make about 1 bowl of soup only. For a larger crowd, increase amounts accordingly. (The original recipe is part of a trio of soups that is meant to feed 4 people).
Bring a pot of salted water to boil and then add the asparagus. Boil until the asparagus begins to float, about 30 seconds. Take off heat, remove asparagus, and set water aside. Put asparagus into a blender and add just enough of the reserved water while blending until it is the consistency of soup. Remove the plastic middle of the blender lid and cover the top with a towel when you turn the blender on to prevent the hot mixture from exploding. Blend the mixture until it is very smooth, adding tarragon as you go. Add salt and pepper to taste.