Preheat the oven to gas 7, 220°C, fan 200°C. Unroll the pastry on to an oiled baking sheet and score a 3cm (1½in) wide border. Prick inside the border with a fork and brush the pastry with a little of the egg. Bake for 12 minutes, until risen and lightly golden.
Meanwhile, heat the butter and oil in a large frying pan. Add the courgettes, onion and garlic. Fry over a medium heat for 6-8 minutes, then stir in the pine nuts.
Gently press down the middle of the pastry, to allow room for the filling. Set aside to cool for 5-10 minutes.
Mix together the crème fraîche with half the Parmesan and the remaining beaten egg. Spread the mixture inside the border and top with the fried vegetables and remaining Parmesan. Return to the oven for 15-20 minutes, until cooked through.