Toast the peppercorns in a hot, dry pan and, once they start to smell fragrant, tip out into a mortar and roughly crush.
Bring a pan of salted water to the boil, ideally use a large wide pan which can fit the pasta in lengthways. This concentrates the starch as much as possible which helps the sauce emulsify. The pasta should be just covered with water, but not by much, so scoop out and discard any excess. Stir the pasta occasionally, to ensure it cooks evenly and, after about five minutes, scoop out about 250ml of the water and set aside to cool slightly while you finely grate the cheese to make the sauce.
Put the grated cheese and most of the pepper into a large, heavy bowl, and anchor it to the work surface with a damp tea towel, if it threatens to slip. Once the pasta is done to your liking (bear in mind that you won’t be cooking it any further after this), drain it well and leave it to cool for a minute while you start the sauce.
Very gradually beat a little of the pasta water into the grated cheese mix to turn it into a paste, then add a little more until you have a sauce the consistency of a bechamel. Add the pasta to the bowl and toss furiously (tongs are very useful here) while also adding enough of the remaining water to make a sauce that coats the pasta – you shouldn’t need all the water.