Brown the chorizo in a skillet over medium heat, breaking it into crumbles as it cooks. Drain excess fat and set aside.
Add the cooked chorizo, onion, garlic, broccoli florets, chicken broth, cumin, chili powder, and smoked paprika to the slow cooker.
Stir to combine, then cover and cook on low for 6 hours until the broccoli is tender.
Stir in the shredded cheddar cheese and heavy cream until the cheese melts and the soup thickens.
Season with salt and pepper to taste, then ladle into bowls and top with chopped cilantro.