Bring a large pan of slightly salted water to the boil while you are preparing the other ingredients.
Add the pasta to the boiling water. While the pasta is cooking, mix the eggs, egg yolks and parmesan together in a bowl and season lightly.
Heat the oil and butter in a large frying pan. Bruise the garlic and add to the pan with the pancetta. Cook over a moderate heat until the pancetta is crisp, discarding the garlic when it becomes golden.
Drain the pasta, reserving a little of the cooking water. Add the pasta to the frying and mix well. Remove from the heat and stir in the egg mixture. Add a spoon or two of the pasta water if the dish looks too dry. Serve immediately with freshly grated parmesan.