Using your hands, squeeze out as much moisture from the zucchini/courgettes as possible. Heat half the oil in a medium non-stick frying pan. Add them to the pan and cook for a further 3-4 mins, until tender. Spoon the vegetables into a large bowl.
Stir in the parsley, cheese and spaghetti and season. Beat the eggs and stir into the mixture.
Heat remaining oil in the frying pan and tip in the spaghetti mixture. Level it out with the back of a spoon and cook over a medium heat for 3-5 mins, until almost set.
Transfer to a hot grill for 2-3 mins, until golden. Leave to cool in the pan for 5 mins, then cut into wedges and serve.