Place chicken in the bottom of a 6-quart slow cooker along with onion, carrots, celery, garlic, bay leaves, salt, pepper, thyme, and rosemary.
Pour in chicken broth and cover. Cook on LOW for 3 hours.
Whisk the cream and flour together until smooth. Add it along with the milk, mushrooms, and rice to the slow cooker. Cook for 1-2 more hours on HIGH (or 2-3 hours on low) or until rice is cooked through. (Cook uncovered on high for the last 30 minutes for a thicker soup.)
Remove the bay leaves, shred the chicken, ladle the soup into bowls, sprinkle with parsley, and serve with bread.
Video
Notes
Keep leftovers in an airtight container in the refrigerator for 4 days, and in the freezer for 4 months.