Dice the onion, carrots, and celery. Season the chicken breast with salt and pepper and add to the slow cooker with the diced vegetables.
Add the wild rice, thyme, rosemary, and bay leaves to the slow cooker.
Pour the chicken stock into the slow cooker and mix everything until the broth covers the entire content of the slow cooker. Cook for 7:30 hours on low.
Once the 7:30 hours have passed, remove the chicken from the slow cooker and shred with forks. The chicken should be easy to shred. Add the shredded chicken back to the slow cooker.
Make a roux to thicken the soup: In a pan on medium heat, add the butter and flour. Once the mixture darkens, add the milk and cream. Add to the roux into the slow cooker.
Add mushrooms and cook on low for 30 minutes. Once 30 minutes have passed, serve with chopped parsley on top.