Place the cubed potatoes, onion, bell pepper, celery, and minced garlic into a 6-quart slow cooker.
Sprinkle the Cajun seasoning and smoked paprika over the vegetables and toss to coat evenly.
Pour the chicken broth over the vegetable mixture.
Secure the lid and cook on LOW for 6 to 8 hours or HIGH for 3 to 4 hours until the potatoes are tender.
Use an immersion blender to pulse the soup 3-4 times for a creamy consistency with remaining potato chunks, or use a potato masher to reach desired texture.
Incorporate the heavy cream and softened cream cheese into the slow cooker, stirring until the cheese is completely melted and the liquid is emulsified.
Season with salt and black pepper; adjust to taste.
Maintain on the WARM setting until service.