In a crockpot, combine the broccoli florets, diced carrots, diced onion, minced garlic, vegetable broth, salt, black pepper, paprika, and cayenne pepper (if using). Stir to combine.
Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the vegetables are tender.
Once the vegetables are cooked, use an immersion blender to puree the soup to your desired consistency. If you prefer a chunkier soup, blend only half of it.
Stir in the heavy cream, shredded cheddar cheese, and grated Parmesan cheese. Mix until the cheeses are melted and the soup is creamy.
Taste and adjust seasoning if necessary. Serve hot, garnished with additional cheese or croutons if desired.