Fry the onion in olive oil until it’s soft/translucent; not too hot so as to avoid discolouration. Reduce the heat then add the garlic and sautée for a minute as the pan cools. Then add the olives, capers, anchovies and cherry tomatoes, mix around (so the anchovies break up) until the ingredients are warm, say about a minute. Then add tomato purée, parmesan and basil, leave on heat until hot enough (no longer – we don’t want the tomatoes to disintegrate). Done. Mix with pasta of choice cooked in parallel. Serve with extra parmesan.
Freshly ground black pepper is also smart.