Heat the extra virgin olive oil in a medium pot over medium heat and sauté the diced onion, carrots, and celery until the vegetables are softened and fragrant.
Add the chicken breast to the pot and sear for 2 minutes on each side to develop flavor.
Pour in the chicken broth and bring the mixture to a gentle boil, then reduce the heat to low and simmer for 15 minutes until the chicken is cooked through.
Remove the chicken breast from the pot, shred it using two forks, and return the shredded meat to the simmering broth.
Stir the dry orzo into the pot and cook for 8 to 10 minutes until the pasta is tender and al dente.
In a small bowl, whisk the large egg and fresh lemon juice together until the mixture is light and frothy.
Slowly temper the egg mixture by whisking in one ladle of the hot broth, then gradually pour the tempered mixture back into the pot while stirring constantly to create a silky texture.
Season the soup with sea salt and black pepper, then garnish with chopped fresh parsley before serving warm.