Start by heating olive oil in a large stock pot over medium heat. Toss in the diced onion, carrot, and celery, and sauté for 8–10 minutes until softened.
Add the minced garlic and stir for another minute to release its fragrance without burning it.
Add the chicken stock and drop in the bay leaves to infuse a robust flavor. Carefully submerge the chicken breasts and bring it all to a gentle boil. Lower the heat and simmer for about 15 minutes, allowing the chicken to cook through and the broth to absorb the aromatics.
Once the chicken has cooked, remove it along with the bay leaves from the pot. Add the orzo to the simmering broth and cook for 10 minutes or until tender.
Meanwhile, shred the chicken with two forks and set it aside to return to the soup later.
Now, it’s time to create that signature creamy texture! Whisk together the egg yolks and fresh lemon juice in a mixing bowl. Slowly ladle in 1–2 scoops of the hot broth while whisking constantly to temper the eggs. This step is critical to avoid curdling.
Return the shredded chicken to the pot, then slowly stir in the tempered egg-lemon mixture.
Keep the heat low and cook for about 5 minutes, letting the soup thicken slightly. Stir in the fresh dill, adjust salt and pepper to taste, and serve it piping hot.