Heat a deep saucepan over high heat. Add a little olive oil and brown the chicken on both sides, starting with the skin side. Once ready, remove and set aside.
In the same pot, add the onion, carrot, and potatoes and sauté until the vegetables are soft, without changing color.
Return the chicken to the pot and add the bay leaf, chicken stock, salt and pepper. Cover and simmer for 40 minutes.
Remove the chicken, add the rice, and continue boiling. While the rice is cooking, debone the cooked chicken.
Beat the eggs in a large bowl for a few minutes. Add corn flour, if using, and as much lemon juice as desired. Seasoning and beat until the mixture is homogeneous.
Slowly pour a ladleful of the soup into the egg mixture, to raise the temperature of the eggs, then pour the mixture into the pot. Simmer over low heat for a few minutes until the soup thickens, stirring constantly.
Serve the soup in deep plates, placing the chicken pieces on top.