Remove chorizo casings and crumble this into a 5- to 6-quart pan; just add the onion and garlic or the onion powder and garlic powder. Stir often over medium high heat until the meat and onion are browned, about 15 minutes.
Mix masa with the chorizo base, then stir in chiles, paprika, and the chicken broth.
Stirring often, bring to a boil over high heat. Simmer gently 20 minutes to blend flavors; stir frequently.
Skim fat from the surface as it accumulates and discard.
Ladle soup into bowls; just add the cheese and cilantro to taste. Serve warm and plain with any main dish, side dish, or appetizer.