Cook the spaghetti in a large pot of boiling water with plenty of salt according to the packet instructions. Reserve a cup of the cooking water before draining.
Heat the olive oil in a wide, rimmed frying pan over medium heat. Add the garlic and anchovies and cook briefly, stirring, until the garlic is just turning golden and the anchovies have broken down into the oil.
Add the tinned tomatoes and cook briefly, then add the capers and olives. Bring to a bubble, then stir through half the parsley and the Calabrian chilli paste.
About four minutes before the pasta is ready, scoop it directly into the sauce using tongs or a pasta spoon, bringing some of the starchy cooking water with it. Toss well, adding more cooking water a splash at a time as needed. Continue cooking for a few minutes until the pasta is done to your liking.
Scatter over the remaining parsley and serve immediately with freshly grated Parmesan and basil lea