Heat a nonstick skillet over medium-high heat with 1 tablespoon oil, 1 turn of the pan. Add chorizo, brown and crumble and remove to paper towel-lined platter to drain.
Heat a nonstick Dutch oven or soup pot over medium-high heat and add 1 tablespoon oil. Add onions, garlic, salt and pepper and stir a couple of minutes. Add beef to brown and crumble. Season beef with oregano, cumin, coriander, chili powder and pimenton and stir another minute. Add broth and bring to boil, then reduce heat to medium low. Stir in cream cheese and crema or cream. Stir in cheeses and melt. Add chilies and tomatoes and gently combine. Add chorizo back to soup. Serve with tortillas and toppings of choice.