Rinse asparagus well. Bend back each stalk, letting stalk snap naturally where tender flesh becomes tough and woody; discard stems. Cut off tips from about one third of spears and reserve for garnish. Cut remaining asparagus into 1-inch pieces. Melt butter in large saucepan over medium-low heat. Add leeks and cover tightly. Cook, stirring occasionally, until tender, about 10 minutes. Add broth, chopped asparagus and potato, and bring to a boil over high heat. Return heat to medium-low and simmer, partially covered, until potatoes are very tender, about 30 minutes. Stir in heavy cream and season to taste with salt and pepper. Meanwhile, bring a medium saucepan of lightly salted water to a boil over high heat. Add reserved tips and cook until barely tender, about 4 minutes. Drain, rinse under cold water and drain again. In batches, puree soup in blender (or use a hand blender to puree soup in pot). Return to pot, if necessary, and add tips. Cook, stirring often, to heat tips through without boiling. (The soup can be prepared up to 1 day ahead, cooled, covered and refrigerated. Reheat gently over low heat, stirring often. If soup thickens upon standing, pour in additional broth to thin soup as needed.) Transfer soup to a warmed soup tureen and serve hot, drizzling each serving with a few drops of heavy cream, if desired.

Serves 8.