Start by preparing your ingredients. Peel and dice the potatoes, chop the onion, and mince the garlic.
In the Crockpot, combine the diced potatoes, broccoli florets, chopped onion, and minced garlic.
Pour in the vegetable broth, and add the olive oil, salt, black pepper, and paprika (if using). Stir to combine all the ingredients.
Cover the Crockpot and cook on low for 6 hours, until the vegetables are tender.
After cooking, use an immersion blender to blend the soup to your desired consistency. If you prefer a chunkier texture, blend only half of the soup.
Stir in the heavy cream and shredded cheddar cheese, mixing until the cheese is completely melted and well incorporated. Allow the soup to heat for an additional 15-20 minutes on low.
Taste the soup and adjust seasoning if necessary. Serve hot, garnished with fresh chives or parsley if desired.