In a crockpot, combine potatoes, broccoli, onion, garlic, and vegetable broth.
Cover and cook on low for 6-7 hours or high for 3-4 hours until potatoes are tender.
Use an immersion blender to partially blend the soup, leaving some chunks for texture.
Stir in heavy cream, cheddar cheese, salt, black pepper, and smoked paprika.
Let cook for an additional 15 minutes until the cheese is melted and the soup is creamy.
Stir in butter for extra richness before serving.
Serve hot with crusty bread or crackers.