01 - Melt butter in a large soup pot over medium heat. Add onion, carrots, celery, and garlic and sauté for 5 to 6 minutes until vegetables are softened.
02 - Sprinkle flour evenly over the softened vegetables and stir constantly for 1 to 2 minutes to form a pale roux.
03 - Gradually whisk in chicken broth, ensuring no lumps remain. Add bay leaf and dried thyme.
04 - Stir in uncooked rice. Increase heat to bring contents to a boil, then reduce to low and simmer, partially covered, for 15 to 18 minutes until rice is nearly cooked.
05 - Add cooked chicken, whole milk, and heavy cream. Simmer gently for 8 to 10 minutes, stirring occasionally, until the soup thickens and rice is tender.
06 - Remove bay leaf. Season with salt and freshly ground black pepper to taste.
07 - Ladle hot soup into bowls and garnish with freshly chopped parsley if desired.