In a dutch oven, warm olive oil over medium heat, then sauté carrots, green onions, celery, and garlic for about 5 minutes until softened. Season chicken with salt and pepper, then add to the pot.
Pour the chicken broth over the chicken to cover, then cover with the lid and bring to a boil. Reduce heat to low and simmer for about 25 minutes, until chicken is cooked through.
Remove chicken from the pot and set aside, then add the rice. Return lid to pot and cook for 20 minutes until rice is tender.
Meanwhile, shred chicken using two forks (or add to your stand mixer and let it do the shredding for you!)
In a medium bowl, whisk together the lemon juice and the eggs. Then slowly whisk in 2 cups of the hot broth, to temper the eggs so they don’t scramble when you add to the soup.
Add the chicken and the sauce to the soup pot, give it all a good stir. Season to taste with salt and pepper
Divide into bowls, garnish with parsley, and eat!