In a large saucepan, bring the broth, celery and parsley to a boil.
Meanwhile, in a small bowl, beat eggs. Beat in flour and enough milk to form a mixture the consistency of cake batter. Drop by teaspoonfuls into boiling broth. Reduce heat to medium-low; cover and simmer for 10-15 minutes or until dumplings are light and not gummy. Season with pepper.