1. In a large pot, melt the butter over medium heat. Sauté the onion, carrots, celery, and mushrooms until softened, about 5-7 minutes.
2. Stir in the flour and cook for 1-2 minutes to form a roux. Slowly whisk in the chicken broth, ensuring there are no lumps.
3. Add the wild rice, thyme, salt, and pepper. Bring to a boil, then reduce to a simmer. Cover and cook for 35-40 minutes, or until the rice is tender.
4. Stir in the shredded chicken and heavy cream. Simmer for another 5-10 minutes until heated through.
5. Serve hot, garnished with fresh parsley and a slice of crusty bread on the side.