In a large pot, bring 6 cups of low-sodium chicken broth to a gentle simmer over medium heat. Add 2 boneless, skinless chicken breasts to the broth and cook for about 20 minutes, ensuring they reach an internal temperature of 165°F. Once tender, remove the chicken from the pot, shred it into bite-sized pieces, and set it aside, keeping the broth simmering.

Using the same pot of simmering broth, add 1 diced onion, 2 minced garlic cloves, 2 sliced carrots, and 2 chopped celery stalks. Sauté the vegetables for 5-7 minutes, stirring occasionally until softened and fragrant.

Stir in 1 cup of rice or orzo into the pot with the sautéed vegetables. Allow the mixture to simmer gently for about 15 minutes, or until the rice or orzo is tender and fully cooked.

In a separate bowl, whisk together 3 large eggs and the juice of 2 freshly squeezed lemons. Gradually add about 1 cup of hot broth from the pot into the egg-lemon mixture while whisking vigorously.

Slowly pour the tempered egg mixture back into the pot with the simmering soup while stirring continuously. Continue to heat the soup gently for a few minutes until it thickens slightly.

Add the shredded chicken back into the soup and season with salt and pepper to taste. Simmer for an additional 2-3 minutes, then garnish with fresh lemon zest and parsley before serving warm.