In a large pot, bring the chicken broth to a boil. Add the chicken breasts (or thighs), onion, carrots, and celery. Reduce the heat to medium-low and let it simmer for 20-25 minutes until the chicken is cooked through and the vegetables are tender.
- Remove the chicken from the pot and shred it using two forks. Set it aside.
- Add the orzo pasta (or rice) to the broth and cook according to package instructions, about 8-10 minutes.
- In a separate bowl, whisk the eggs with the lemon juice and zest until smooth and frothy.
- Gradually temper the egg-lemon mixture by slowly adding a ladle of the hot broth from the pot, whisking constantly to prevent curdling.
- Slowly pour the egg mixture into the pot, stirring constantly. Let it cook on low heat for an additional 5 minutes, ensuring the soup thickens but does not come to a boil.
- Add the shredded chicken back into the pot and stir to combine. Taste the soup and adjust seasoning with more salt or pepper if needed.
- Serve the soup hot, garnished with fresh parsley.