01 - Melt butter in a large soup pot over medium heat. Add chopped onion, diced carrots, celery, and minced garlic. Sauté for 5 to 6 minutes until the vegetables are softened.
02 - Sprinkle flour evenly over the softened vegetables. Stir constantly for 1 to 2 minutes to create a smooth roux, ensuring the flour is fully incorporated and lightly cooked.
03 - Gradually whisk in chicken broth to prevent lumps. Incorporate the bay leaf and dried thyme, mixing thoroughly.
04 - Stir in uncooked long-grain white rice. Bring mixture to a boil, then reduce to low heat and simmer, partially covered, for 15 to 18 minutes or until rice is nearly tender.
05 - Add shredded cooked chicken, whole milk, and heavy cream. Simmer gently for 8 to 10 minutes, stirring occasionally, until soup thickens and rice is fully cooked through.
06 - Remove the bay leaf. Adjust seasoning with salt and black pepper according to taste. Serve hot, garnished with fresh parsley as desired.