Bring broth to a full boil in a 3- or 4-quart saucepan over medium-high heat. Add rice and stir constantly until broth returns to a boil. Reduce heat; cover and simmer 12 minutes or until rice is tender.

Meanwhile to make avgolemono mixture, whisk eggs and lemon juice in a small bowl. Slowly stir 1 cup of hot broth into egg mixture, then stir into saucepan. Stir over low heat until soup coats a wooden spoon. Be sure soup does not boil.

Taste soup; add salt and pepper if needed.