1. Cook the spaghetti in plenty of boiling,well-salted water until al dente (start testing at 8 minutes). Now get everything else ready,because when the pasta is cooked,it's go-go-go.
2. Whisk the whole eggs and egg yolks in a large bowl. Season with sea salt,then whisk in pepper and all but 1 tablespoon of the cheese.
3. Thickly slice the ham and shred into small,bite-sized pieces. Heat the oil in a deep frypan and fry the ham briskly until crisped at the edges. Drain the spaghetti (saving half a cup of the pasta water) and add immediately to the ham,tossing well to coat.
4. Tip the spaghetti and ham into the egg mixture and toss furiously until well-combined,letting the heat of the pasta'cook'the eggs into a cheesy,almost creamy,sauce. Add a slosh or two of the pasta cooking water as you toss,to lighten the sauce.
5. Serve immediately on warm plates and scatter with remaining cheese and extra black pepper.
This recipe featured in theGood Food Christmas television special on Nine.