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 saute briefly then stir in the garlic.
Add the chicken broth then raise the heat to high. Add bay leaves. Once the liquid has come to a 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.
Combine egg and lemon the following way: in a medium bowl, whisk together the lemon juice and eggs. While whisking add 2 ladles-full of the broth from the cooking pot (this helps temper the eggs). Once fully combined, add the sauce to the chicken soup and stir. Remove from the heat immediately.
Serve hot with your favorite bread. Garnish with parsley. Enjoy!