In a large stockpot or Dutch oven set over medium heat, add butter. Once the butter has melted, add the celery, carrots, onion and mushrooms. Cook until tender, about 5-7 minutes.
Add flour and stir constantly until cooked, about 1 minute. Slowly pour in chicken broth, whisking continuously until all of the broth has been added. Turn heat up to medium-high and bring mixture to a simmer.
Add salt, garlic powder, pepper, thyme and parsley. When the mixture is bubbling, add rice. Let rice boil for 1 minute, then cover and reduce heat to low. Cook for 15 minutes or until rice is cooked throughout.
Add shredded chicken and continue cooking for 5 minutes, then pour in the milk, mix and bring 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 compliments the wild rice really well.