Heat a dutch oven or large soup pot over medium high heat. Add the onion, celery, and carrots and toss to coat in the fat. Saute, stirring occasionally, until the onions are translucent and the carrot and celery soften, 7-8 minutes.

Pour in the chicken broth, then season with the salt, pepper, and oregano. Add the bay leaf, then bring the liquid to a simmer. Add the chicken breasts, cover the pot, and simmer until the chicken is cooked through to at least 165°F, 20-25 minutes depending on the thickness of the chicken breasts. Remove the chicken and shred.

Temper the eggs. Whisk the eggs and lemon juice in a large mixing bowl or 4-cup measuring cup. While vigorously whisking the lemon and egg mixture, slowly pour in ½ cup of hot broth directly from the pot. Continue whisking and slowly adding three more ½-cup additions of broth, until the mixture is very smooth and has cooled to room temperature.

Return the shredded chicken to the pot, along with the cauliflower rice. Simmer 3 minutes, or until the cauliflower rice is warmed through and completely defrosted.

Turn off the burner and remove from heat. Pour the tempered egg mixture into the soup, then stir to combine. Taste for seasoning and adjust the salt, pepper, and lemon juice to taste. Remove the bay leaf.

Ladle into bowls, garnish with fresh parsley or dill and lemon zest if desired. Enjoy!