1. To make the pastry, place the flour, sugar, salt, butter and Parmesan in a food processor and pulse to make fine crumbs. Slowly add the egg, pulsing between additions, until the mixture comes together as a soft dough. If it’s still a little dry, add 1 tsp of cold water at a time and pulse again until you reach the correct consistency.
2. Turn the dough out onto a lightly floured surface. Roll out to fit a 25cm x 5cm deep loose-bottomed tin. Transfer the dough to the tin, press into the edges and remove any excess pastry around the top. Repair any cracks or holes with the pastry cuttings. Place in the freezer for 30 minutes to chill whilst you make the filling.
3. Preheat the oven to 200°C, gas mark 6 and place a baking sheet in the oven to warm up. To make the filling, use a vegetable peeler to make long, thin carrot and courgette ribbons. Mix with the onion. In a bowl, whisk the eggs, extra yolks, cream and cheese together, then season with salt, white pepper and nutmeg. Set aside.
4. Fill the chilled pastry case with baking paper and baking beans. Place onto the preheated baking tray in the oven and bake blind for 20 minutes. Remove the paper and the beans and bake for a further 5 minutes, until golden. Remove from the oven, leaving the baking sheet behind.
5. Working from the outside in, layer the vegetables, on their sides, into the pastry case. Pour over the egg mixture. Place carefully back onto the baking sheet in the oven and cook for 30-40 minutes, or until just set and golden, covering the pastry edges with foil during cooking if they become too brown. Leave to cool in the tin for 20 minutes before removing. Cut and serve while still warm with a dressed green salad.