01 - Combine chicken, broth, onion, garlic, carrot if using, and salt in a large pot. Bring to a boil over medium-high heat.
02 - Reduce heat to a simmer. Cover and cook for 15-20 minutes until chicken is cooked through.
03 - Remove chicken from the pot and set aside. Add rice to the simmering broth. Cook uncovered for 15 minutes until rice is tender. While rice cooks, shred the chicken into bite-size pieces using two forks.
04 - Whisk together eggs and lemon juice in a medium bowl until smooth.
05 - Gradually ladle 1 cup of hot broth into the egg-lemon mixture, whisking constantly to temper the eggs.
06 - Slowly pour the tempered egg-lemon mixture back into the pot, stirring gently. Return shredded chicken to the soup. Heat over low do not boil for 2-3 minutes until slightly thickened and creamy.
07 - Season with additional salt and pepper to taste. Ladle into bowls and garnish with fresh dill or parsley.