Heat the olive oil in a large saucepan or frying pan (with a lid) over a medium heat.
Add the chopped chorizo and fry for about 5 minutes until it starts to release its oils and go brown.
Add the onions and garlic and fry gently for 4–5 minutes until they are softened.
Add the dry pasta, chopped tomatoes, paprika, oregano, salt, pepper, tomato puree, broccoli, and cherry tomatoes.
Pour in 500 ml (2 cups) of the vegetable stock and stir everything well.
Cover the pan with the lid and cook for about 15 minutes.
Check the pasta during cooking, and if it looks dry before the pasta is cooked through, add more stock from the reserved amount as needed.
Once the pasta is cooked and most of the liquid is absorbed, stir in the grated Parmesan cheese, garnish with fresh basil, and serve immediately.