Bring a large pan of salted water to the boil, then add the spaghetti and cook according to packet instructions.
Meanwhile, place a large frying pan over a medium–high heat. Add a good lug of olive oil, followed by the garlic, anchovy and chilli. Tear in the olives and stir for 2 minutes, or until the garlic starts to turn golden and the anchovies melt into the base. Add the cherry tomatoes, a good splash of pasta water and cover with a lid. Cook for 3 to 4 minutes, or until the cherry tomatoes start to cook down slightly.
Drain the pasta, reserving a cupful of cooking water. Add the basil to the sauce along with the pasta and a splash of the reserved cooking water, to loosen. Have a taste and season if needed. Transfer to a serving platter and top with a good shaving of fresh Parmesan.