Dice the carrots, celery, and onion. Slice mushrooms and mince garlic.
Rinse the wild rice blend under cool water and drain.
Add carrots, celery, onion, mushrooms, and garlic to the slow cooker.
Add wild rice, thyme, rosemary, bay leaves, salt, and pepper.
Place chicken over the vegetables and rice.
Pour in 6 cups chicken broth.
Cover and cook on LOW for approximately 6–7 hours or HIGH for 3–4 hours, checking according to your rice blend and slow cooker.
Once the chicken is fully cooked and the rice is tender, remove the chicken and discard bay leaves.
Shred chicken into bite-size pieces.
Melt butter in a small saucepan over medium-low heat.
Whisk in flour and cook for about 1 minute.
Gradually whisk in whole milk and cook gently until slightly thickened.
Stir in heavy cream.
Pour the creamy mixture into the slow cooker and stir.
Return shredded chicken to the soup.
Cover and cook on HIGH for another 15–20 minutes.
Add additional warm chicken broth if the soup is thicker than desired.
Taste and adjust salt and pepper.
Stir in fresh parsley.
Serve warm.