Slice the courgettes lengthwise
Make the tomato sauce by simmering the tomatoes for half an hour, seasoned with salt and origano, in the minimum of water, then pass through a sieve; the sauce is not dense.
Beat up the fresh eggs, dip the courgette slices in the egg, then in flour, and fry lightly in hot oil, to brown them.
Oil an earthenware casserole, put a layer of courgettes on the bottom, season, add a few thin slices of mozzarella and a little of the sauce, cover the layer with more courgette slices, season, add sliced hard-boiled egg, some mozzarella and some sauce, and repeat until all is used up.
Cover the top with fine oven-dried crumbs and grated parmesan, and pour over it a thread of olive oil. Bake in a moderate oven for half an hour.
Aubergines can be prepared in the same way.