01 - In a large soup pot, melt unsalted butter over medium heat. Add finely chopped onion, diced carrots, diced celery, and minced garlic. 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 - Gradually whisk in chicken broth to prevent lumps. Add bay leaf and dried thyme, stirring well to combine.
04 - Stir in the uncooked long-grain white rice. Bring the mixture to a boil, then reduce heat and simmer partially covered for 15 to 18 minutes, or until rice is nearly tender.
05 - Fold in cooked shredded chicken, whole milk, and heavy cream. Simmer gently for an additional 8 to 10 minutes, allowing the soup to thicken and rice to become fully cooked.
06 - Remove and discard the bay leaf. Season generously with salt and freshly ground black pepper to taste.
07 - Ladle hot soup into bowls. If desired, garnish with chopped fresh parsley before serving.