In Greek communities, this soup is known as Avgolemono.
Combine stock and rice in soup kettle, cover tightly, and simmer 20 minutes. (Don’t peek at rice as it cooks.) Remove from heat. In small bowl combine egg yolks and lemon juice. Beat with whisk until smooth. Pour 1 cup hot soup into egg and lemon mixture, stirring slowly and constantly until blended. Return mixture to soup kettle and continue stirring slowly for several minutes over low heat until mixture is smooth. (Do not let soup boil after egg and lemon have been added or it will curdle.) Cool, chill, and serve cold, garnished with paper-thin slices of lemon. (Also good hot.)