Prep all of the ingredients by washing produce, chopping and mincing.
Heat a large stock pot over medium heat. Add oil and allow to heat for 30 seconds-1 minute.
Add chopped celery, carrot, onion to the pot. Sauté for 3-4 minutes, stirring frequently. Add your minced garlic and continue to cook for 30 seconds.
Pour in chicken broth and bring to a simmer. Once simmering, add chicken breasts to the pot with tongs. Turn heat down to medium-low.
Season with salt and pepper. Cover and continue simmering the soup for 30 minutes.
After 30 minutes, remove the chicken breasts and set aside on a plate. Add the rice to the pot.
Add the 2 eggs yolks to a medium-sized bowl. Remove 1 cup of the broth from the soup, and 1 tbsp at a time, slowly whisk in the soup broth to the egg yolks, whisking the eggs the entire time. This is called tempering the eggs, and it allows them to be added to the soup without scrambling them. Once tempered, add the egg and broth mixture to the soup.
Shred the chicken using two forks. Add the shredded chicken back to the soup.
Allow the soup to sit on low for 4-5 minutes to thicken. Just be very careful not to bring it back to a boil now that the eggs have been added.
Right before eating, stir in the fresh dill and lemon juice. When serving, garnish with fresh parsley!