Preheat 4 serving plates. Bring a large saucepan of salted water to the boil and add 1 tablespoon of the olive oil and the spaghetti. Cook the pasta according to the instructions on the packet - it should be tender but still firm to the bite.

Peel and chop the onion. Heat the rest of the oil in a frying pan and briefly fry the bacon until just cooked on both sides. Remove the bacon from the pan, leaving the cooking juices behind. Add the onion to the pan and cook for 4 minutes over a medium heat, stirring occasionally, until it softens and begins to turn golden.

While the onion is cooking, chop the bacon into large squares and discard the rinds. Grate the cheese onto a plate, then beat the eggs thoroughly with a fork in a small bowl.

When the onions are cooked, add the bacon squares and milk or cream to the pan and season to taste. Reduce the heat.

Drain the cooked spaghetti and return it to the pan. Quickly stir in the beaten eggs and the grated cheese. Stir in the remaining ingredients and divide between the heated plates.

Garnish with the parsley and extra twists of black pepper, and serve.