01 - Melt unsalted butter in a large soup pot over medium heat. Add the onion, carrots, celery, and garlic; sauté for 5 to 6 minutes until vegetables are softened.
02 - Sprinkle all-purpose flour evenly over the vegetables, stirring constantly for 1 to 2 minutes to create a roux without browning.
03 - Gradually whisk in chicken broth, ensuring the mixture stays lump-free. Add the bay leaf and dried thyme.
04 - Stir in the uncooked rice. Bring to a boil, then reduce heat and simmer, partially covered, for 15 to 18 minutes until rice is almost tender.
05 - Add the cooked chicken, whole milk, and heavy cream. Simmer gently for 8 to 10 minutes, until the soup thickens and rice is fully cooked.
06 - Remove and discard the bay leaf. Season with salt and black pepper according to preference.
07 - Ladle the soup into bowls and serve hot. Garnish with fresh parsley if desired.