To a 6-quart (or larger) slow cooker, add the potatoes, ham, celery, carrots, onion, cream of chicken soup, mustard powder, salt, pepper, parsley, garlic powder, oregano, bay leaves, and chicken broth. Stir to combine everything evenly.
Cover and cook on low for 7 hours or high for 3–4 hours, until the potatoes are tender.
Thicken the soup (optional): For a thicker, creamier soup, use a potato masher to mash some of the potatoes right in the slow cooker before adding the cream.
Stir in the frozen peas and heavy cream. Cover and continue cooking for another 30 minutes on low or 15 minutes on high, until everything is heated through.
Add cheese (optional but delicious): Remove the bay leaves, then stir in shredded cheddar cheese until melted and creamy.
Ladle into bowls and top with extra cheese or chopped parsley if you like. Serve with crusty bread or buttery biscuits for the perfect meal.