Add potatoes, carrots, celery, onion, ham, salt, pepper, parsley, garlic, and broth. Stir well to combine.
Cover crockpot with lid and cook on low for 6-7 hours or on high for 3-4 hours until vegetables are tender.
Turn off crockpot and add heavy whipping cream or milk. Using a potato masher, mash the vegetables to help thicken the soup. If you want a more thicker soup, you can add a slurry of corn starch and broth from crockpot.
Garnish with cooked bacon, cheese, green onions, and/or sour cream.