Bring a large pot of salted water to a boil. Add chicken, bouillon, celery, parsley and salt and pepper to taste. Cook for 45 minutes or until chicken is no longer pink inside. Reduce heat to low and continue to simmer.
To Make Dumplings: While chicken is cooking, combine the flour, egg, sour cream, and chicken broth in a medium bowl. Mix well and roll dough out on a floured surface. Cut into small squares and drop into boiling chicken broth. In a small bowl, mix together corn starch and enough water to form a thin paste; stir into broth. Continue to simmer for 5 to 10 minutes, or until dumplings are light and puffy.
