01 - Melt butter in a large soup pot over medium heat. Add onion, carrots, celery, and garlic. Cook, stirring occasionally, for 5 to 6 minutes until vegetables are softened.
02 - Sprinkle flour evenly over sautéed vegetables and cook, stirring constantly, for 1 to 2 minutes to form a smooth roux.
03 - Gradually whisk in chicken broth to ensure the mixture stays lump-free. Stir in bay leaf and dried thyme.
04 - Stir in the uncooked rice. Bring mixture to a gentle boil, then reduce heat to low, covering partially. Simmer for 15 to 18 minutes, until rice is nearly tender.
05 - Add cooked chicken, whole milk, and heavy cream. Continue to simmer gently for an additional 8 to 10 minutes, allowing the soup to thicken and rice to finish cooking.
06 - Remove the bay leaf. Season base with salt and black pepper to preferred taste. Serve hot, garnished with fresh parsley if desired.