1. Heat a large stock pot or dutch oven over medium-low heat. 
2. Add 2 teaspoons olive oil.  Once the oil begins to shimmer and the onion, celery and carrot.
3. Saute onion, celery and carrot and season with 1/4 teaspoon of kosher salt.  Continue to cook until vegetables just begin to soften, about 5 minutes. 
4. Add the rice and brown along with the vegetables for about 3-5 minutes. 
5. Add the broth and water and bring to a boil.
6. Turn the heat down to low and simmer for 30 minutes, allowing the rice to cook.  *If you prefer to use white rice rather than brown rice, reduce the simmer time to 15 minutes.
7. Add chicken and simmer for an additional 5 minutes.
8. Meanwhile beat together 2 eggs, egg yolk, 1/2 teaspoon kosher salt and lemon juice. 
9. Add egg mixture to the soup and stir constantly for 1 minute. 
10. Simmer for 5 minutes.
11. Season to taste with salt and pepper and serve.

Alternative for Roasted Chicken:

If leftovers are not on hand, substitute with chicken breast fillets. 

1. Cut breast fillets into bite size pieces and season with salt and pepper.  I also like to sprinkle with a little Cajun Seasoning for a little kick. 
2. Heat a large pot over medium heat. 
3. Add 1/2  teaspoon of olive oil and working in small batches, quickly brown chicken pieces. 
4. Remove from pan and continue until all chicken is browned. 
5. Set cooked chicken aside and proceed with recipe above.