Combine the potatoes, ham, onion, garlic, corn, chicken broth, salt, thyme, rosemary, and pepper in a large slow cooker.
Stir gently to combine.
Cook on high for 3 to 4 hours or low for 6 to 8 hours. You want the potatoes to be nice and tender.
Use a potato masher to gently mash some of the potatoes in the slow cooker or, alternately, scoop out about 4 cups of the potatoes and ham, along with enough liquid to cover them, and blend until smooth and creamy.
Pour the blended potatoes back into the slow cooker.
Stir in the heavy cream and reduce heat to low.
Serve immediately or let soup simmer for another hour or s.
Ladle the soup into bowls and garnish with toppings if desired.