In a medium sized pot, boil 4 quarts of water and cook the shredded chicken until fork tender, approximately 25 minutes.
Meanwhile, in the dutch oven, melt the butter on a medium heat, then add in the carrots, celery, garlic, onion. Sauté until fragrant, approximately 5-8 minutes, then lower the flame to a medium-low heat.
Pour in the broth, the rice, and fresh thyme, stir.Add the shredded chicken, then cover and cook on a low flame to a simmer or until the rice is fully cooked through, approximately 35-40 minutes.
Approximately 15-20 minutes before the soup is done cooking, whisk together the whole milk and flour to form a slurry, then pour into the soup and stir. Finish cooking for an additional 20 minutes.
Season to taste then serve with crusty bread.
Notes
Remember to use enough liquid so that it does not get too thick once the rice is added. You still want a little movement in the soup from the liquid instead of being globby and clumpy. Yes, I said globby.Season as you go. Its important to balance out the soup from being under-salted to having enough flavor from the acid, heat, fat, and the salt.Different types of rice require different lengths of cooking, but typically you'll want to leave room for the rice to cook through for approximately 20ish minutes. It's up to you to rinse the rice ahead of time which will cut the cook time by a few minutes.