Break off and discard tough asparagus bottoms. Break off tips; set aside. Coarsely chop stalks; cook in skillet with onion in butter, salting lightly. After 8 to 10 minutes, when onions are clear, sprinkle with flour. Continue to stir over lowest possible heat 5 to 8 minutes. Slowly add water or stock, stirring constantly. Cook 8 to 10 minutes stirring frequently, until thickened. Cool slightly. In blender, puree sauce bit-by-bit with milk until thoroughly smooth. Return puree to 3-quart panpreferably a double boiler. Add dill, salt, pepper and tamari. Heat gently but don't boil. As it heats, cook asparagus tips in boiling water until tender, but still very green, about 2 minutes; drain. Add whole to soup.