Coarsely grate the courgettes, then place in a sieve over a bowl. Press to squeeze out all the liquid – this may take a few mins, but try to drain away as much as you can.
Cook the pasta in boiling salted water following pack instructions. Meanwhile, heat a large, non-stick frying pan, then dry-fry the bacon, stirring often, until crisp. Add the chilli and cook for 1 min more, then tip in the courgettes and cook on a high heat for 2-3 mins.
Mix together the egg yolks, cheese, cream and lemon zest. When the pasta is cooked, drain it, reserving a little of the cooking water. Tip everything back into the pasta pan and toss together. Divide into bowls to serve, with extra Parmesan.