Heat the olive oil in a large pot over medium heat. Add the diced onion, carrot, and celery, and sauté for 8-10 minutes, stirring occasionally, until the vegetables are softened and the onion becomes translucent. This slow cooking of the aromatic vegetables (called a mirepoix) creates a flavorful foundation for the soup. Add the minced garlic and cook for 1 minute more until fragrant.

Add the bay leaves, chicken pieces, and chicken stock to the pot. Bring to a boil, then reduce heat and simmer gently for 15 minutes until the chicken is fully cooked through. The chicken will be tender and easy to shred at this stage. I like to keep the heat at a gentle simmer rather than a rolling boil to keep the broth clear and the chicken from becoming tough.

While the chicken finishes cooking, prepare the egg-lemon mixture (avgolemono) that will enrich and thicken the soup. In a small bowl, whisk together the egg yolks and lemon juice until well combined and smooth. Set aside. Once the chicken has finished cooking, carefully remove it from the pot with a slotted spoon and set aside on a cutting board. Remove and discard the bay leaves. Add the orzo to the broth and cook for 10 minutes until tender, stirring occasionally to prevent sticking.

Shred the cooked chicken into bite-sized pieces using two forks or your hands. Once the orzo is tender, carefully ladle about 1 cup of the hot broth into the bowl with the egg-lemon mixture while whisking constantly. This tempering process gradually raises the temperature of the eggs so they don't scramble when added back to the soup. Continue whisking until the mixture is smooth and pale.

Pour the tempered egg-lemon mixture back into the pot with the orzo and broth, stirring constantly to create a creamy, slightly thickened soup. Remove from heat immediately and stir in the fresh dill. Season with salt and black pepper to taste. I find that the lemon juice naturally provides a lot of acidity, so I go easy on the salt and taste as I go—this soup tastes best when the bright lemon flavor really shines through.

Ladle the soup into bowls and serve immediately while hot. The soup is best enjoyed fresh, as the delicate egg-lemon texture is at its best right after cooking.