While preparing the ingredients, bring a large pan of salted water to the boil. Add the spaghetti and cook according to package instructions.
Heat the oil in a large frying pan and add the red onion, garlic, and chilli.
After frying for a few minutes, add in the olives, capers, and seaweed. For a little extra flavour, add in a spoonful of the caper brine. Stir well, cook for a couple of minutes, and then add the halved cherry tomatoes, salt, and pepper.
Cook for around 6-8 minutes until the tomatoes have broken down to create a thick sauce, adjusting the seasoning if necessary. Top tip: Add some of the pasta cooking water to the sauce. The salty, starchy water helps to season and thicken it, and stops it from drying out. You can keep adding spoonfuls of the pasta cooking water until you're ready to plate up.
Once the pasta is cooked, drain it and stir it through the puttanesca sauce, coating evenly. Serve with fresh basil, vegan parmesan, and a drizzle of extra-virgin olive oil.