Dice the onion, carrot, and celery into similar-sized pieces. Mince the garlic cloves. Cube the chicken breasts into 1-inch pieces.
Heat the olive oil in a large pot over medium heat, then add the diced onion, carrot, and celery. Cook for 8-10 minutes until softened.
Add minced garlic and cook for 1 minute until fragrant.
Pour in the chicken stock, add bay leaves and cubed chicken, and bring to a boil. Reduce heat to medium-low and cover the pot.
Simmer gently for 15 minutes until chicken is cooked.
Remove chicken and bay leaves. Add orzo to simmering broth and cook for 10 minutes.
Whisk egg yolks and lemon juice in a bowl. Gradually temper the mixture with hot broth.
Slowly pour the egg mixture back into the pot while stirring continuously.
Shred the cooked chicken and return it to the pot. Add dried oregano and stir.
Simmer gently for 2-3 minutes over low heat.
Stir in fresh dill and season with salt and pepper.
Ladle soup into bowls and top with extra dill. Serve immediately.