Heat the oil in a large frying pan. Add the courgettes and cook over a medium heat for 10 minutes, stirring frequently. Add the sugar and season with salt.
Put a baking sheet in the oven and preheat to 200˚C (gas 6). Lightly grease a 1.5 litre soufflé dish with a small knob of the butter.
Melt the remaining butter in a saucepan over a low heat. Add the flour and cook for 30 seconds, stirring with a wooden spoon. Gradually pour in the milk and bring to the boil, stirring constantly, until thickened. Stir in the cheese until melted, then season with nutmeg, salt and pepper. Remove the pan from the heat and leave to cool.
Whisk the egg whites until stiff. Beat the egg yolks into the cooled sauce, then fold in the courgettes and egg whites. Pour the mixture into the buttered soufflé dish and sprinkle the cheese over the top.
Set the dish on the hot baking sheet and bake for 40–45 minutes or until risen and golden brown. Serve immediately.