01 - In a large soup pot, melt the unsalted butter over medium heat. Add onion, carrots, celery, and garlic. Sauté for 5–6 minutes, stirring occasionally, until vegetables become tender.
02 - Sprinkle the all-purpose flour evenly over the softened vegetables. Stir constantly for 1–2 minutes to blend and eliminate any raw flour taste.
03 - Gradually whisk in the chicken broth to prevent clumping, scraping any bits from the pot. Add the bay leaf and dried thyme.
04 - Stir in the uncooked rice. Bring mixture to a gentle boil, reduce heat, and simmer partially covered for 15–18 minutes until rice is nearly tender.
05 - Add the cooked chicken, whole milk, and heavy cream. Simmer uncovered for an additional 8–10 minutes, stirring occasionally, until the soup thickens and rice is fully cooked.
06 - Remove the bay leaf. Adjust seasoning with salt and black pepper to preferred taste.
07 - Serve hot in bowls. For added freshness, garnish with chopped parsley if desired.