Cook the spaghetti al dente (it should have a bite to it) in a small amount of well-salted water. Reserve about a ½ cup of the pasta cooking water (!).
Prepare the ingredients: finely chop the garlic, roughly chop the anchovies, drain and rinse the capers, cut the olives in half. If you're using crushed tomatoes in a can and not tomato passata/puree I recommend mixing the tomatoes until smooth (with blender or hand blender) - this is optional but I prefer a smooth sauce without tomato chunks.
Heat the olive oil and butter in a large frying pan, add the garlic, chili flakes, and anchovies, cook over medium heat, stirring, for 1 minute.
Add the olives, capers, tomatoes/passata, and pasta cooking water. Bring to a boil, reduce the heat to low and cook for 15 minutes (stirring from time to time) until the sauce has thickened. After this time, season the sauce lightly with salt and pepper. Be careful with adding salt (!), because anchovies, olives, and capers are already salty. Take the pan off the heat.
Add the cooked pasta to the pan, toss with the sauce.
Sprinkle with chopped parsley and serve immediately.