Start by preparing all your ingredients. Peel and dice the potatoes, chop the broccoli into florets, dice the onion, and mince the garlic.
In the crockpot, combine the diced potatoes, broccoli florets, onion, garlic, vegetable broth, salt, black pepper, and paprika (if using). Stir to combine.
Cover the crockpot with its lid and cook on low for 6 hours or until the potatoes and broccoli are tender.
Once cooked, use an immersion blender to blend the soup until smooth, or carefully transfer to a blender in batches (be cautious with hot liquids).
Return the blended soup to the crockpot (if using a blender) and stir in the heavy cream. Let it warm through for an additional 15 minutes.
Gradually add in the shredded cheddar cheese, stirring until fully melted and combined. Adjust seasoning if necessary.
Serve the soup hot, garnished with additional cheese, croutons, or chopped green onions if desired.