In a large pot, heat the olive oil over medium heat. Sauté the chopped onion, carrots, and celery until softened, about 5 minutes. Add the minced garlic and cook for 1 more minute.

Pour in the chicken broth and add the whole chicken breasts. Bring to a gentle boil, then reduce heat, cover, and simmer for 15 minutes until the meat is cooked through.

Carefully remove the meat and shred it with two forks. Return the shredded meat to the pot along with the orzo pasta. Simmer for 10 minutes until the pasta is tender.

In a medium mixing bowl, vigorously whisk the eggs and fresh lemon juice until frothy. While whisking constantly, very slowly drizzle in two ladles of the hot broth to temper the eggs.

Remove the pot from the heat. Slowly stir the tempered egg mixture into the pot until the broth becomes creamy. Stir in the fresh dill, season with salt and pepper, and serve immediately.