Preheat the oven to 200°C.
Roll out the pastry on a lightly floured surface to 1cm thick and cut a round of pastry 3-4 inches larger than an 8 inch springform fluted tart tin.
Line the flan case using the pastry, pressing in well then prick the base. Trim any overhanging pastry and chill for 10 minutes. Line the pastry case with nonstick baking paper and fill with baking beans.
Bake in the oven on a baking sheet for 15 minutes until golden at the edges. Remove the paper and beans at this point, brush the base with the beaten egg and return to the oven to allow the base to cook and brown for 5 minutes. Remove from the oven and cool on a wire rack.
Prepare the filling by whisking together the milk and crème fraîche. Whisk in the 3 beaten eggs and season well with salt and pepper. Stir in the cubed cheese, then arrange the slices of courgette evenly across the base of the pastry.
Pour the filling in and bake the quiche at 170°C for a further 15-20 minutes until the filling is just set. Remove from the oven and allow to cool on a wire rack before turning out and serving on the wire rack. Slice into wide portions and serve.