Combine the olive oil, ground beef and chorizo in a skillet over medium-high heat. Cook, stirring, until browned, 5 to 6 minutes. Season with salt and pepper.
Add the onion and garlic to the skillet and cook, stirring, until softened, about 4 minutes. Clear a space in the pan and add the tomato paste, chili powder, cumin, coriander and paprika; cook, stirring, until incorporated. Add the tomato sauce and 1 cup water; stir everything together and simmer until thickened, 6 to 7 minutes.