In a large pot, heat a splash of olive oil over medium heat. Add the chopped onion, carrots, and celery, and sauté until softened, about 5-7 minutes.
Add the minced garlic and cook for an additional minute until fragrant.
Pour in the chicken broth, and bring the mixture to a boil. Once boiling, add the chicken breasts and reduce to a simmer. Cook for about 20 minutes, or until the chicken is cooked through.
Remove the chicken from the pot and set aside to cool slightly. Once cool, shred the chicken using two forks.
Return the shredded chicken to the pot, then add the orzo pasta. Cook for an additional 8-10 minutes until the orzo is tender.
In a bowl, whisk together the eggs, lemon juice, and lemon zest until well combined.
To temper the egg mixture, gradually add a ladleful of hot soup to the egg mixture while whisking continuously. This will prevent the eggs from curdling.
Slowly stir the tempered egg mixture back into the pot of soup, stirring constantly until well combined and slightly thickened.
Stir in the chopped fresh dill and season with salt and pepper to taste.
Notes
Serve garnished with lemon slices and dill sprigs for a fresh touch.