The name of this classic soup comes from its two main ingredients: egg (avgo) and lemon (lemoni).
In a large saucepan, bring 6 cups stock to a boil. Add orzo; cook until al dente, 10 minutes. Add salt and pepper.
Dissolve cornstarch in 1/2 cup water. Heat remaining 2 cups stock until hot; do not boil.
In an electric mixer, beat eggs with whisk until fluffy; add cornstarch mixture and lemon juice. With mixer on medium-low speed, slowly add one to two cups hot stock until incorporated and mixture thickens slightly. Add any remaining stock to orzo.
Over low heat, slowly add egg mixture to orzo, stirring constantly until thickened and creamy. Do not let it come to a boil; the eggs will curdle. Serve immediately.