Heat the olive oil in a large pot or Dutch oven over medium heat. Once shimmering, add the diced onion, carrots, and celery. Cook for about 5 to 6 minutes, stirring occasionally, until the vegetables have softened and the onion is translucent. Add the minced garlic and cook for another 30 seconds until fragrant.

Add the chicken breasts or thighs directly into the pot in a single layer. Pour in the chicken broth and water, then sprinkle in the dried thyme, oregano, garlic powder, onion powder, salt, and black pepper. Bring everything to a boil over medium-high heat, then reduce the heat to medium-low and let the soup simmer for about 18 to 20 minutes, or until the chicken is fully cooked through.

Remove the chicken from the pot and set it on a cutting board. Using two forks, shred the chicken into bite-sized pieces and set aside. While the chicken is resting, increase the heat to medium and add the orzo to the simmering broth. Cook for 8 to 9 minutes, stirring occasionally so the orzo doesn't stick to the bottom.

While the orzo cooks, prepare your lemon egg mixture. In a small bowl, whisk together the two eggs, lemon juice, and lemon zest until smooth and well combined. This is the step that gives the soup its signature creamy, bright flavor without adding any dairy.

Once the orzo is cooked, reduce the heat to low. Slowly ladle about one cup of the hot broth into the egg and lemon mixture while whisking constantly. This tempers the eggs so they don't scramble when added to the soup. Slowly pour the tempered mixture back into the pot, stirring gently as you go.

Return the shredded chicken to the pot and stir everything together. Taste the soup and adjust salt and pepper as needed. Stir in the fresh parsley just before serving. Ladle into bowls and enjoy right away while it's hot.