Snap off asparagus tips and set the stalks aside. Melt butter in a deep skillet with a cover. Add asparagus tips, onion, leeks, celery and potato. Cover lightly and cook over the very lowest heat until vegetables are soft, 20 minutes or more.
Meanwhile, place chicken stock in a large saucepan with the reserved asparagus stalks, cut into large pieces. Bring to a boil and simmer, covered tightly, for about 30 minutes. Discard stalks and set stock aside.
In a food processor, puree softened vegetables and add to the asparagus stock. Season with lemon juice, salt, white pepper and paprika, if desired. Allow to cool and refrigerate. Stir in half-and-half and serve garnished with a dollop of creme fraiche or whipped cream and a sprinkling of paprika, if desired.