Bring broth to a boil in a medium-sized pot.  Mix cornstarch with 1 tablespoon water and pour into broth.  

Beat eggs well with a fork in a small bowl and slowly stream in eggs with the tines of the fork, stirring with the fork after each addition. 

Season the soup with white pepper, and garnish with green onions.  

If serving with wontons, add to soup, simmer for 20 minutes and serve.