Sauté veggies: In a large pot, melt butter and sauté onion, garlic, celery, and carrots until soft (about 5–6 minutes).
Add flour (if using): Stir in flour and cook for 1 minute to form a light roux.
Pour in broth & add rice: Stir slowly while adding the chicken broth. Add rice and thyme.
Simmer: Now boil the soup, reduce the heat and simmer it gently for at least for 25 minutes until you get the perfectly cooked.
Add chicken & cream: Stir in shredded chicken and milk or cream. Simmer on low for 5–7 minutes.
Adjust seasonings: Add salt, pepper, and optional veggies. Cook for another 2–3 minutes.
Rest & serve: Let it sit for 5 minutes before serving to allow it to thicken naturally.