Place onions, carrots, celery, chicken, wild rice, mushrooms, and dried thyme in the slow cooker insert.
Pour in the chicken stock. Cover and cook on high for 6 hours or low for 8 hours.
About 45 minutes before soup is ready, pour in the milk.
Melt butter in a small saucepan. Add all-purpose flour and stir constantly for 2 minutes. Then add 1 cup (240ml) water and continue to stir.
Immediately pour this mixture into the soup.
Add salt and pepper. Then give it a good stir. If soup is a little too thick, add a little more chicken stock or water to desired consistency. Cover and allow soup to finish cooking in the slow cooker.
Stir in chopped parsley just before serving.