Cook spaghetti to packet instructions in salted boiling water (about 8 minutes)
While spaghetti is cooking, slice the chorizo into thick discs, then cut the discs into quarters. Fry the sliced chorizo in a little olive oil in a large frying pan for about 5 minutes then turn the heat to it's lowest setting.
Lightly whisk the eggs in a bowl and stir in the grated cheese and generous amount of black pepper. When the pasta is cooked, use tongs (or drain in a sieve and reserve a quarter cup of the cooking liquid) and place the pasta in the frying pan with the chorizo and turn OFF the heat.
Pour the egg and cheese mixture over the pasta and using the tongs (or a fork), keep lifting and moving the pasta around the pan, add a tablespoon or two of the cooking liquid and the residual heat of the pasta will warm the eggs through to make a sauce.
After a few minutes of moving the pasta around the eggs will emulsify. If they haven't come together, you can put the pan on a very low heat for a minute (stirring and lifting the pasta constantly!) to help the eggs thicken - but be careful; if it gets too hot the eggs will scramble!
Please note - parmesan does contain animal products; so for an easy vegetarian alternative omit the chorizo and swap the cheese for a vegetable-based one.Serve with a side salad if you like!