Place the chicken breasts in the bottom of the slow cooker.
Add the wild rice, carrots, celery, onion, garlic, chicken broth, thyme, rosemary, parsley, salt, and black pepper.
Cover and cook on Low for 6 to 7 hours or High for 3 to 4 hours, until the chicken is cooked through and the rice is tender.
Remove the chicken and shred it with two forks.
Return the shredded chicken to the slow cooker.
Whisk together the cornstarch and cold water until smooth, then stir it into the soup.
Pour in the heavy cream and stir well.
Cover and cook for another 20 to 30 minutes until the soup thickens slightly.
Garnish with fresh parsley before serving.