01 - Place the chicken, mushrooms, carrots, celery, onion, garlic, wild rice, thyme, rosemary, bay leaf, salt, and black pepper into the slow cooker.
02 - Pour in the chicken broth and stir everything together to distribute evenly.
03 - Cover and cook on LOW for 6 to 7 hours or on HIGH for 3 to 4 hours, until the chicken is fully cooked through and the wild rice is tender.
04 - Transfer the chicken to a plate and shred using two forks, then return the shredded meat to the slow cooker.
05 - Melt the butter in a small saucepan over medium heat, then whisk in the flour and cook for 1 to 2 minutes to form a smooth roux.
06 - Gradually whisk the heavy cream into the roux and heat until the mixture thickens, then stir it into the slow cooker.
07 - Stir well, re-cover, and continue cooking on LOW for an additional 20 to 30 minutes until the soup is creamy and heated throughout.
08 - Remove and discard the bay leaf, taste the soup, and adjust seasoning as desired. Serve hot.