Heat the avocado oil in a large thick-bottomed pot such as a Dutch oven over medium-high heat on the stove top. Add the chopped yellow onion and cook, stirring occasionally, until the onion begins to soften, about 3 to 5 minutes.

Stir in the chopped carrots, celery, and garlic and cook for another 2 to 3 minutes to soften the veggies.

Place the chicken breasts on top of the vegetable medley and sprinkle with sea salt and black pepper.

Pour in the chicken broth into the pot and add the bay leaves. Cover the pot and bring it to a full boil.

Reduce the heat to medium-low and cook for 15 minutes to poach the chicken, or until the chicken is cooked through. Remove the chicken breasts from the pot and place them on a cutting board. Ladle a small amount (about ½ cup) of the broth into a small bowl and set it aside. This hot broth will be used to temper the egg yolks.

Pour the uncooked white rice into the pot, cover, and return the soup to a boil. Reduce to low heat and continue cooking for 15 minutes.

While the rice is cooking in the soup, transfer two egg yolks to a small bowl and whisk them together. Pour the reserved broth into the bowl with the egg yolks along with the fresh lemon juice and mix well to temper the yolks. Pour the egg mixture into the pot with the rest of the soup and stir well. Continue cooking the soup with the egg-lemon mixture until the rice is fully cooked and the 15 minutes is up.

Use two forks to shred the chicken and add the chicken back into the pot with the soup once it is all shredded.

Taste the soup for flavor and add sea salt, black pepper, or more lemon juice to taste.

Remove the bay leaves and discard. Stir in the fresh chopped dill.

Serve soup in big bowls with crusty bread or a side salad.