In a large slow cooker, add the first 8 ingredients (potatoes through, and including, the chicken stock).
Stir, cover, and cook on LOW for 8-10 hours, or high for 4-5 hours or until potatoes are tender.
Once the potatoes become tender, in a small bowl or closed canning jar, whisk together, or shake milk and cornstarch until smooth.
Stir the mixture into the ham and potato soup in the Crockpot.
Cover and cook on HIGH 20-25 minutes until thickened, stirring occasionally.
Turn off heat, stir in cheese, sour cream and parsley until cheese is melted.
Serve sprinkled with extra cheese, sour cream and parsley, if desired.