Heat the olive oil and butter over medium heat in a large Dutch oven.
Add the minced garlic and cook until fragrant, about 1 minute. Stir in the leeks, onion, carrots, and celery. Cook for 5–7 minutes, until softened.
Pour in the chicken broth, and add the bay leaves, thyme, rosemary, oregano, and crushed red pepper flakes (if using).
Stir in the rice and bring the soup to a simmer. Let it cook for about 15 minutes, or until the rice is tender.
(If using raw chicken breasts, add them to the pot and simmer for 15 minutes, until fully cooked.
Remove, shred with two forks, and return to the soup. If using cooked shredded chicken, stir it in and let it warm through.)
Lower the heat and stir in the heavy cream and lemon juice. Let the soup warm gently for another 2–3 minutes. Season with salt and black pepper to taste.
Ladle the soup into bowls and top with fresh parsley and dill. Serve with lemon wedges for an extra pop of brightness and a side of crusty bread.