Start by preparing your vegetables. Chop the broccoli, onion, celery, and carrots into small pieces and mince the garlic.
In a pan, melt the butter and whisk in the flour to create a roux. Cook for 1-2 minutes until the mixture is bubbly and thick.
Slowly add in the broth, whisking constantly, until the mixture is smooth. Transfer the mixture to your crock-pot.
Add in the vegetables, salt, pepper, paprika, and cayenne pepper. Stir to combine.
Cook on low for 6-8 hours or high for 3-4 hours, until the vegetables are tender.
About 30 minutes before the soup is done, add in the milk, heavy cream, and Velveeta cheese. Stir until the cheese is melted and the soup is creamy.
Serve hot and enjoy!