For the pastry, sift the flour and salt into the bowl of a food processor. Add the shortening and butter and process until the mixture resembles fine breadcrumbs.
Add the egg yolk and pulse, the mixture should come together to form a dough. If your mixture is too dry add a little water and pulse again.
Tip the pastry out onto a lightly floured work surface and briefly knead. Bring the pastry together in a ball, place in a plastic bag and refrigerate for 20-30 minutes.
Meanwhile prepare the filling, place the apples in a saucepan and add the lemon juice to prevent them browning. Add the plums.
Mix the cornflour with the sugars, allspice, cinnamon and grated nutmeg. Place in the pan with the fruit and toss to coat the fruit in the dry mix.
Place over a medium heat and cook until the sugars melt to form a caramel. Bring to a gentle simmer for two minutes then set aside to cool.
Preheat the oven to 180C/350F/Gas 4.
Lightly flour a work surface and rolling pin. Remove the pastry from the fridge and set aside one-third for the pie lid. Roll out the remaining pastry until it is big enough to generously fit the pie dish (approximately 40cm/16in). Use the rolling pin to help you lift the pastry into the pie dish and gently press it into the sides, leaving any excess pastry overhanging the sides. Return to the fridge to chill for a few minutes.
When chilled, remove the pastry case from the fridge and place on a baking tray. Line with baking parchment and fill with baking beans and then bake for approximately 10 minutes, or until the pastry is just beginning to colour and dry out. Remove the baking parchment and baking beans.
Lightly whisk the egg white and brush over the pastry to glaze. Return the pastry to the oven and cook for a further five minutes, or until the pastry is a pale golden-brown and dried out.
Roll out the remaining pastry for the pastry lid, using a plate to cut a circle that is roughly the correct size. Use any excess pastry to form a 1x26cm/½x10½in strip and shapes to decorate the pie.
Trim the excess pastry from the edge of the pie dish - leaving about 1cm/½in of the pie dish rim showing.
Using a slotted spoon, place the cooled fruit into the pastry case, discarding any excess liquid.
Place the thin strip of pastry on top of the exposed rim of the pie dish. Brush with a little water, then place the pie lid on top and trim to shape.
Crimp the edges to seal and place the decorative shapes on top. Cut a small hole in the middle to let any steam escape while cooking.
Glaze with milk and sprinkle with sugar. Bake for 40-45 minutes, or until the pastry is golden-brown and crisp.