01 - In a large soup pot, melt unsalted butter over medium heat. Add finely chopped onion, diced carrots, diced celery, and minced garlic. Sauté for 5 to 6 minutes, stirring occasionally, until vegetables are soft and fragrant.
02 - Sprinkle all-purpose flour evenly over sautéed vegetables. Stir constantly for 1 to 2 minutes, allowing the flour to coat the vegetables and cook lightly.
03 - Gradually whisk in chicken broth to prevent lumps. Add bay leaf and dried thyme, stirring to combine.
04 - Stir in long-grain white rice. Bring mixture to a boil, then reduce heat to low. Partially cover and simmer for 15 to 18 minutes until rice is almost tender.
05 - Add cooked chicken, whole milk, and heavy cream to the pot. Stir gently and simmer for an additional 8 to 10 minutes until soup is thickened and rice is fully cooked.
06 - Remove bay leaf. Season soup with salt and black pepper to taste.
07 - Ladle soup into bowls and serve hot. Optionally, garnish with fresh parsley.