Cook the pasta according to package and reserve one cup of the cooking water before draining.
Meanwhile heat a splash of olive oil in a large pan over medium heat. Add the garlic, chili and the anchovies and fry them for 3-4 minutes, until the anchovies have almost melted into the oil.
Add the tomato passata and let it cook until the sauce has thickened, about 10 minutes.
Add the olives, capers and cherry tomatoes. Mix well.
Now adjust the seasoning with salt and pepper if needed (the sauce will already be quite salty due to the anchovies).
Add the cooked pasta to the pan and mix well. Add some of the pasta cooking water, if the spaghetti are too dry for your taste.
Sprinkle with the chopped parsley and serve immediately with parmesan.