In a medium saucepan stir together water, instant chicken bouillon granules, fresh lemongrass or lemon peel, fresh cilantro, and white pepper; bring to boiling. Reduce heat to low; cover and simmer for 15 minutes. Strain the liquid, discarding the solids; return the liquid to the saucepan.
Return liquid to boiling. Set aside a few of the asparagus tips for garnish. Add the remaining asparagus to saucepan. Reduce heat to low and simmer about 8 to 10 minutes or until asparagus is tender. Remove from heat; cool slightly. Carefully transfer mixture to a blender container; cover and blend until smooth. Set aside.
In the same saucepan gradually stir milk into cornstarch. Cook and stir over medium heat until thickened and bubbly; cook and stir for 2 minutes more. (The mixture may be slightly foamy.) Gradually add the asparagus mixture, stirring constantly. Heat through.
Ladle the asparagus soup into soup bowls. Swirl a little sour cream into each serving, if desired, and top with reserved asparagus tips. Makes 6 side-dish servings.