Place the diced potatoes, onion, garlic, and sun-dried tomatoes into the slow cooker.
Add the vegetable broth, oregano, rosemary, salt, and pepper. Stir to combine.
Cover and cook on low for 6 to 7 hours or on high for 3 to 4 hours until the potatoes are soft.
Stir in the chopped kale and heavy cream. Cover and cook for another 20 to 30 minutes until the kale wilts.
Ladle into bowls and top with grated Parmesan cheese before serving.