Heat the olive oil in your large pot over medium heat. Add the diced onion, carrot, and celery, cooking until the onion becomes translucent and the vegetables soften slightly, about 5 minutes. Stir in the minced garlic and cook for another minute until fragrant.
Add the chicken breasts to the pot and pour in the chicken broth. Bring everything to a gentle boil, then reduce to a simmer. Allow the chicken to cook through, roughly 15-20 minutes. Once cooked, remove the chicken breasts and set them aside to cool slightly.
While the chicken cools, add the orzo pasta to the simmering broth. Cook it uncovered for about 8 minutes or until tender but still firm (al dente). Keep an eye on the broth level; if it reduces too much, add a splash of water or additional broth.
Using two forks, shred the cooled chicken breasts into bite-sized pieces. Return the shredded chicken to the pot with the orzo and broth.
In a medium bowl, whisk together the eggs, lemon juice, and lemon zest until smooth and frothy.
To prevent the eggs from scrambling, slowly ladle about one cup of hot broth from the pot into the egg-lemon mixture, whisking constantly.
Slowly pour the tempered egg mixture back into the pot, stirring gently but continuously. Heat the soup on low for a few more minutes, but do not let it boil. Taste and season with salt and pepper as needed.
Ladle the soup into bowls and sprinkle generously with fresh chopped parsley.
