In a Dutch oven (5 quart), heat olive oil over medium-high heat. Add the onion and saute until soft and translucent, about 2 minutes. Add garlic and cook for 30 seconds.
Reduce the heat to low, and add chicken stock, bay leaves, and lemon rind. Add the chicken to the broth, along with rice, and salt, and cook at a very gentle simmer for 15 minutes.
Remove the chicken from the broth onto a cutting board and allow it to cool. When it’s cool enough to handle, shred it with two forks.
Remove the bay leaves and lemon rind and discard.
In a medium bowl or glass jug, whisk together the eggs and egg yolks, add the lemon juice and whisk until combined. Takes 2 full ladles (one by one) from the chicken stock, and gradually add to the egg mixture while whisking. This will temper the eggs so it’s safe to add the mixture to the soup.
Pour the mixture into the soup while stirring to combine. Add the shredded chicken, and cook over low heat for 5 minutes.
Taste for lemon and salt; add more if desired. Stir in dill, or save it for garnish. Remove from heat, and serve.
