Place the first 4 ingredients in a pot and gently simmer until the vegetables are quite tender. Puree the mixture in a food processor, and then transfer to a bowl. Stir in the tarragon, salt and white pepper. Chill at least 4 hours in the fridge. Ladle the soup into chilled bowls; top with a dollop of sour cream. If desired, garnish the top with a few blanched asparagus spears or with a sprinkle of chopped chives.
Options: Make the soup vegetarian by using vegetable stock instead of chicken. Use chopped fresh dill to flavour the soup instead tarragon. Make chilled white asparagus soup by using it to make the soup instead of green. Be sure to peel the tougher skinned white asparagus before slicing and cooking until very tender.