Bring chicken broth to a gentle boil and add rice or orzo. Cook until tender.
Stir in cooked shredded chicken and heat through.
In a bowl, whisk eggs until frothy, then gradually whisk in fresh lemon juice.
Slowly add a ladle of hot broth to the egg mixture while whisking continuously to temper the eggs.
Gradually pour the tempered mixture back into the soup, stirring constantly.
Heat gently over low heat without boiling to keep the soup smooth and creamy.
Garnish with fresh parsley and black pepper before serving.