Start your soup base. In a large pot or Dutch oven, heat olive oil over medium heat. Add the diced onion, carrots, and celery (if using) and sauté for about 5 minutes until softened but not browned. Add the garlic and cook for another 30 seconds until fragrant. Your kitchen should already be smelling amazing!
Build the broth. Pour in the chicken broth and bring to a gentle boil. Season with salt, pepper, and dried oregano. Reduce heat to maintain a simmer.
Cook the chicken. Add the whole chicken breasts to the simmering broth. Cook for about 15-20 minutes until the chicken is completely cooked through (internal temperature of 165°F/74°C). Remove the chicken to a plate and once cool enough to handle, shred or dice it into bite-sized pieces.
Add the rice. While the chicken is cooling, add the uncooked rice to the simmering broth. Cook according to package directions until tender, usually about 15-20 minutes.
Prepare for the magic moment. In a medium bowl, whisk the eggs until frothy. Slowly add the lemon juice while continuing to whisk. This is your avgolémono mixture, and it's about to transform your soup!
The crucial technique - tempering. This is where the magic happens! Take about 2 cups of the hot broth (just the liquid, not the rice) and very slowly add it to the egg-lemon mixture, whisking constantly. This step is called "tempering" and prevents the eggs from scrambling. Go slowly – we want silky soup, not egg drop soup!
Bring it all together. Once your egg-lemon mixture is tempered, slowly pour it back into the pot with the remaining soup, stirring constantly. Keep the heat on low – do not let it boil again or the eggs might curdle. Add the shredded chicken back to the pot.
Finish with fresh herbs. Stir in the fresh dill and parsley. Taste and adjust seasonings, adding more salt, pepper, or lemon juice as needed.
Serve with style. Ladle into bowls and garnish with additional fresh dill, a twist of black pepper, and lemon slices. Congratulations – you've just made one of Greece's most beloved soups!