Line a 21cm x 11cm rectangular baking tray with baking parchment and preheat the oven to 180C, gas mark 4.
In a large bowl, combine flour, baking powder, sugar and softened vegan butter/spread. Add 1 vegan egg substitute of choice (I used "Orgran No Egg" egg replacer) and combine. Wrap the dough in clingfilm and chill in the fridge for 10-15 minutes before using.
Whilst the dough is cooling, make the filling. Quarter, core, peel and slice the apples about 5mm thick. Place in a medium saucepan, add cinnamon, cardamom and 1-2 tablespoon(s) of water. Cook over medium heat for around 15 minutes or until soft and mushy stirring occasionally. If the apple mixture is too sour, add sugar or maple syrup.
Roll out 3/4 of the pastry so that it is big enough to cover the bottom of the tin. Cover the pastry with the stewed apple mixture.
Roll out the remaining pastry that was set aside. Slice into strips to create a lattice effect on top of the pie. Carefully lay the lattice pie top over the top. Bake in the middle of the oven for around 45 minutes or until golden. Allow to cool then sprinkle with a little icing sugar before cutting into 8 squares.