01 - In a large pot, melt butter over medium heat. Add onion, carrots, celery, and garlic. Sauté for 5 to 6 minutes until vegetables are softened.
02 - Sprinkle flour over the sautéed vegetables, stirring constantly for 1 to 2 minutes until a smooth roux forms.
03 - Gradually whisk in chicken broth to prevent lumps. Add bay leaf and thyme, stirring to combine.
04 - Stir in uncooked rice. Bring mixture to a boil, then reduce heat to low and simmer, partially covered, for 15 to 18 minutes or until rice is nearly tender.
05 - Add cooked chicken, whole milk, and heavy cream to the pot. Simmer gently for another 8 to 10 minutes until soup thickens and rice is fully cooked.
06 - Remove bay leaf. Season with salt and black pepper to taste.
07 - Ladle soup into bowls and serve hot. Garnish with fresh parsley if desired.