Brown the Chorizo: Heat the olive oil in a large, high-sided frying pan over medium heat. Add the chorizo and cook until golden and the fat has rendered. Remove the chorizo to a bowl, leaving about 1 tablespoon of the flavourful oil in the pan.
Cook the Aromatics: Add the onion to the same pan and cook for about 5 minutes until soft and translucent. Add the garlic and cook for another minute.
Build the Sauce: Stir in the tomato purée and oregano and cook for 1–2 minutes. Pour in the passata and 300 ml boiling water, then return the chorizo to the pan and stir well.
Cook the Pasta: Add the dry rigatoni directly to the sauce and bring to a gentle boil. Reduce the heat, cover and simmer for about 12–15 minutes, stirring occasionally, until the pasta is al dente and the sauce has thickened. *If the sauce becomes too thick before the pasta is cooked, add a splash of hot water and continue simmering.
Finish and Serve: Taste and adjust the seasoning if needed. Divide between bowls and finish with grated Parmesan, torn mozzarella and fresh basil.