Chop onion, garlic, celery and carrot.
Add chopped vegetables, salt, pepper, bay leaf and oil in a large pot (big enough for the chicken it to move around in broth but not too big). Saute on medium-high heat for 5 min.
Add chicken and fill pot with enough water to cover it by 2 cm. Cover and bring to the boil. Once boiling, reduce heat to low and simmer for 45 min - 1 hr.
Once the chicken is cooked - the meat should pull away from the bones easily. Remove chicken and when cooled enough to handle, roughly remove meat. Remove 1 cup of broth and set aside.
Bring the broth to a simmer, add salt to taste and add rice. Reduce heat and allow to simmer for 15-20 min or until rice is cooked. Turn off heat.
With a fork, whisk together 50 g or 1.8 oz lemon juice and egg yolks in a measuring jug. Using the cooled 1 cup of broth, slowly whisk it into the egg mixture.
Return chicken meat to broth and slowly drizzle in egg mixture.
Serve with fresh chopped parsley, extra lemon juice and salt to taste.