Start by making the pastry. Place the plain flour, icing sugar and salt in a large bowl and whisk to mix or place in a food processor and pulse until combined.
Add the cold diced vegan block butter and rub it in using your fingers or blend with the food processor until the mixture resembles fine breadcrumbs and no lumps of fat remain.
Add the cold vodka (or water) and mix; drizzle in a little cold water as needed to bring the pastry together into a ball. Divide the pastry in half and shape each half into a disc.
Cover the pastry discs and pop them in the fridge for half an hour until it has firmed up a bit.
Once the pastry has chilled prepare the filling. Peel and core the apples then cut them into thin slices. Place them in a large bowl and toss with the grated ginger and lemon juice then add the plain flour, cornflour, light brown soft sugar, granulated sugar, cinnamon, stem or crystallised ginger and salt. Mix until everything is well combined. Set aside.
Roll out one of the pastry discs on a lightly floured surface to about 3mm thick then carefully transfer it to a 23cm / 9 inch round, 5 cm / 2 inch deep pie dish. Press the pastry into the corners and up the sides and trim off the excess, leaving about 3cm / 1 inch overhanging. Reserve the trimmings.
Transfer the apple filling to the pie dish, piling it high and discarding any juices that have collected in the bottom of the bowl.
Roll out the other half of the pastry to about 3mm thick. If you wish to make a lattice crust, use a pizza cutter or sharp knife to cut it into strips. They can all be the same width or you can vary the width as I did. You can also cut thin strips and braid them together.
Using your two longest strips, lay on the tart to make a cross in the centre – don’t attach the strips to the edges. The strip that’s vertical as you look at it should be on top.
Lay two strips of pastry horizontally, either side of the horizontal strip.
Fold the middle horizontal strip back on itself to the left and put a vertical strip on the tart to the right of the folded back strip. Unfold the pastry strip back to its original position, then repeat on the other side.
Now repeat with the vertical strips: fold up the middle vertical strip, put a horizontal strip at the bottom, then fold back the middle strip. Repeat this process on all sides until the pie is covered. You can re-roll the pastry trimmings to cut more strips if needed.
Press all the edges down to seal using a drop of water to help them stick, then trim off the excess.
Fold the overhanging pastry back over itself so that it covers the ends of the lattice strips, press it down to seal then crimp the edge. Place the pie in the fridge for 20 minutes while you preheat the oven to 200°C/180°C fan/400°F/gas mark 6.
Brush the top of the pie with non-dairy milk and sprinkle with caster or granulated sugar. Bake for 60-75 minutes until the apples are tender (a knife pushed into the filling should go in easily) and the filling is bubbling. You can loosely cover the pie with tin foil part way through baking if the pastry starts to get too dark before the apples are cooked.
Remove the pie from the oven and leave to cool, uncovered, for 3 hours before serving.