In a large stockpot or Dutch oven set over medium heat, add the butter. Once the butter has melted, add the celery, carrots, onion, and mushrooms. Cook until tender, about 5–7 minutes.
Add the flour and stir constantly until cooked, about 1 minute. Slowly pour in the chicken broth, whisking continuously until all of the broth has been added. Turn the heat up to medium-high and bring the mixture to a simmer.
Add the salt, garlic powder, pepper, thyme, and parsley. When the mixture is bubbling, add the rice. Let the rice boil for 1 minute, then cover and reduce the heat to low. Cook for 15 minutes or until the rice is cooked throughout.
Add the shredded chicken and continue cooking for 5 minutes, then pour in the milk, mix, and bring the mixture back to a simmer. Allow the soup to simmer until thick, about 5 additional minutes.
Remove from the heat and let cool for 10 minutes before serving.
Notes
*You can add more mushrooms. I like to add just enough to give the soup a more earthy flavor. It complements the wild rice really well.STORE leftovers in an airtight container in the refrigerator for up to 4 days. To FREEZE, transfer it to a freezer-safe container or bag and freeze for up to 2 months.Thaw overnight in the fridge and REHEAT gently on the stovetop over medium-low heat, stirring occasionally. Add a splash of broth or milk if the soup becomes too thick.