Put abundant water on to boil for the pasta, waiting for it to come to a boil before salting it. Add the pasta and cook following the package instructions, though start checking it a good 2 minutes before it's meant to be ready.
While the pasta is cooking, make the sauce by putting all the remaining ingredients, bar the basil, into a processor and blitzing until you have a nubbly-textured sauce.
Just before draining the pasta, remove a cupful of pasta-cooking water and add 2 tablespoonfuls of it down the funnel of the processor, pulsing as you go.
Tip the drained pasta into your warmed serving bowl. Pour and scrape the sauce on top, tossing to coat (add a little more pasta-cooking water if you need it) and strew with the basil leaves.