Don’t peel the courgettes unless they are elderly. Slice into thick pennies and strew with salt, leaving them in a colander or on a tilted plate for an hour or so, to drain off some of their moisture.
Heat the oil and butter in a large frying pan, and toss the dried courgettes, a few at a time, without browning them. Keep them warm. Melt a little more butter and oil and cook the chopped