Melt butter in a heavy saucepan over medium heat. Add leeks, celery and onion. Reduce heat and cover. DO NOT ALLOW THE VEGETABLES TO COLOR. Sweat the vegetables until they are translucent. Add the potatoes and the stock. Bring to a boil. Reduce heat and continue to simmer lightly until the potatoes are very soft. Add the asparagus and cook only until the asparagus is tender. Remove from heat and cool slightly. Using a blender, puree until smooth. Chill.

Before serving remove from the refrigerator and stir in cream. Season with salt and pepper, to taste. Garnish with reserved cooked asparagus tips.