Place the chicken breasts in the bottom of the crockpot.
Add the potatoes, carrots, celery, onion, garlic, chicken broth, thyme, parsley, rosemary, salt, and black pepper.
Cover and cook on Low for 6 to 7 hours or High for 3½ to 4 hours, until the chicken is cooked through and the vegetables are tender.
Remove the chicken and shred it using two forks.
Return the shredded chicken to the crockpot.
Stir in the frozen peas, softened cream cheese, and heavy cream.
Whisk together the cornstarch and cold water until smooth, then stir it into the soup.
Cover and cook for another 20 to 30 minutes until the soup thickens.
Serve topped with baked puff pastry squares or warm biscuits and garnish with fresh parsley.