Add chicken, vegetables, rice and seasoning to slow cooker. Add chicken broth and water. Cover and cook for 4 to 5 hours on HIGH setting or 7 to 8 hours on LOW setting.
When chicken is done, remove from slow cooker onto a plate. Shred. Return to slow cooker.
In a saucepan, melt butter. Add milk and cornstarch. Whisk and cook until thickens, about 7 minutes. Add mixture to soup in slow cooker and stir well. Add more water if needed.
Serve soup with crusty bread or croutons. Garnish with fresh chopped parsley.