• First, peel and trim the asparagus, reserving the trimmings. Bring stock or broth to a simmer in a large saucepan. Then, add trimmings and let stand 15 minutes.
• Next, rinse spears, pat dry and cut into 1 1/2 pieces, reserving tips. Strain stock or broth into a large saucepan and add the asparagus stalks, potato, shallot, and salt and pepper to taste.
• Bring the liquid to a boil over high heat and simmer the mixture, stirring occasionally, for 25 minutes, or until asparagus is tender.
• Meanwhile, in a saucepan of boiling salted water blanch the asparagus tips until just tender, drain and refresh.
• In a food processor or blender puree the soup in batches until smooth, correct seasoning and return to saucepan. Heat until hot.

To serve: ladle soup into bowls and garnish with reserved asparagus tips, sour cream, lemon peel and dill.