In a large Dutch oven or heavy pot, heat 1 tbsp. olive oil on medium-high. Add the carrots, celery, and green onions, toss together to sauté briefly then stir in the onion. Add the chicken broth and bay leaves then raise the heat to high. Once the liquid has come to a rolling boil, add the rice, salt, and pepper. Turn the heat to medium-low and simmer for 20 minutes or until the rice is tender. Now stir in the cooked chicken. To prepare the egg-lemon sauce, in a medium bowl, whisk together the lemon juice and eggs. While whisking add 3 ladles-full of the broth from the cooking pot (this helps temper the eggs so they won’t curdle when you add the sauce to the soup). Once fully combined, add the sauce to the chicken soup and stir. Remove from the heat immediately. Garnish with fresh parsley, if you like. Serve hot with your favorite crusty bread.