Using a food processor shred the courgettes using the 'julienne' setting. You could use a grater but it is hard work.
Put a about a tablespoon of oil in the bottom of a large heavy pan and add one knob of butter. Put the pan on the heat and add the grated courgette. As the courgette begins to cook stir it carefully, moving the stuff from the bottom and allowing some from the top to reach the heat. In a minute or two the courgette wilts and begins to soften, releasing some juice. Add a little salt.
Using a slotted spoon, fish out all the courgette into a sieve or colander and allow the juice to drain back into the pan.
Turn up the heat and boil the juice only, reducing it by evaporation. When it has almost reduced and is thicker (this may take a few minutes it depends how overripe the courgettes are) add the second knob of butter and the juice of half a lemon.
To serve plop the courgettes from the sieve onto a dish and tip over the sauce. Grind over a bit of pepper.
Old courgettes that are large contain more water than young courgettes and it is important to be patient and reduce the released juice properly so that it is thickish and almost evaporating.