01 - In a large soup pot, melt unsalted butter over medium heat. Add 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 softened vegetables and stir constantly for 1 to 2 minutes to form a smooth roux.
03 - Gradually whisk in chicken broth, ensuring no lumps remain. Add bay leaf and dried thyme, mixing well.
04 - Stir in uncooked long-grain rice. Bring mixture to a boil, then reduce heat and simmer partially covered for 15 to 18 minutes, or until rice is almost tender.
05 - Add cooked chicken, whole milk, and heavy cream to the pot. Simmer gently for an additional 8 to 10 minutes, allowing soup to thicken and rice to become fully cooked.
06 - Remove the bay leaf. Season the soup generously with salt and freshly ground black pepper to taste.
07 - Ladle soup into bowls and serve hot. Garnish with freshly chopped parsley if desired.