Cook the Chicken: In a large pot, add the chicken breasts, chicken broth, and water. Bring to a boil, then reduce the heat and simmer until the chicken is cooked through, about 20 minutes. Remove the chicken, shred it, and set aside. Reserve the broth.

Prepare the Vegetables: In the same pot, heat the olive oil over medium heat. Add the chopped onion, carrots, and celery. Sauté until the vegetables are tender, about 5-7 minutes.

Cook the Orzo: Add the orzo pasta to the pot and cook for about 8-10 minutes, until it’s al dente.

Prepare the Egg-Lemon Mixture: In a bowl, whisk together the eggs and lemon juice.

Temper the Eggs: Slowly add a ladleful of hot broth to the egg-lemon mixture, whisking continuously to prevent the eggs from curdling. Repeat with another ladleful of broth.

Combine and Finish: Slowly pour the tempered egg mixture back into the pot, stirring constantly. Add the shredded chicken back into the pot. Cook for another 5 minutes, ensuring the soup is heated through but not boiling. Season with salt and pepper to taste.

Serve: Ladle the soup into bowls, garnish with fresh parsley, and serve hot.