01 - In a large soup pot, melt unsalted butter over medium heat. Add the onion, carrots, celery, and garlic, and sauté for 5 to 6 minutes until vegetables are softened.
02 - Sprinkle all-purpose flour over the sautéed vegetables, stirring constantly for 1 to 2 minutes to form a smooth roux.
03 - Slowly whisk in chicken broth to the pot, ensuring no lumps. Add the bay leaf and dried thyme.
04 - Add the uncooked long-grain white rice. Bring to a boil, then reduce heat, cover partially, and simmer for 15 to 18 minutes until rice is almost tender.
05 - Add cooked chicken, whole milk, and heavy cream. Simmer gently for 8 to 10 minutes, allowing the soup to thicken and rice to finish cooking.
06 - Remove the bay leaf. Season with salt and black pepper according to taste preferences.
07 - Ladle hot soup into bowls. Garnish with fresh parsley if desired and serve immediately.