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 vegetables are softened.
02 - Sprinkle flour over softened vegetables. Stir constantly for 1 to 2 minutes until combined, allowing the flour to cook gently.
03 - Gradually whisk in chicken broth while stirring to prevent lumps. Add bay leaf and dried thyme.
04 - Stir in uncooked rice. Bring the mixture to a boil, then reduce heat to a gentle simmer. Cover partially and cook for 15 to 18 minutes or until rice is nearly tender.
05 - Add cooked chicken, whole milk, and heavy cream. Simmer gently for 8 to 10 minutes, stirring occasionally, until the soup is creamy and rice is fully cooked.
06 - Remove the bay leaf. Season with salt and black pepper to taste.
07 - Ladle soup into bowls and serve hot, garnished with fresh parsley if desired.