Line a large baking sheet with a layer of paper towels. Quarter, core, peel and slice apples quite thin (about 5 mm thick) and lay onto paper towels. Set another layer of paper towels on top, to absorb any liquid. Set aside.
For pastry, beat 225 g butter and 50g sugar in a large bowl until just mixed. Add one whole egg, and one yolk (reserve white for later). Beat together for 1 minute. Work in flour with a wooden spoon, 1/3 at a time until it starts to clump together, then mix in the rest with your hands. Form into a ball and wrap with plastic wrap. Chill dough 45 minutes.
Mix 140g sugar, cinnamon, and flour in a large bowl.
Once pastry has chilled, heat oven to 170 degrees Celsius Lightly beat egg white with a fork. Cut off one third of the pastry and keep it wrapped while you roll out the rest.
Line a 20-22 cm pie dish with pastry, leaving a slight overhang. Roll remaining third to a circle about 28cm (to cover, with a couple of cm.s to spare).
Pat apples dry with kitchen paper. Tip apples into bowl with cinnamon-sugar mixture and toss through. Pile high into pastry-lined pie dish.
Brush a little water around the pastry rim and lay pastry lid over the apples, pressing edges together to seal. Trim edges with a sharp knife and make 5 small slashes on top of lid to allow steam to escape.
Brush pie with egg white and sprinkle with sugar. Bake 40-45 minutes until golden.
Sprinkle with more sugar and serve warm with ice cream or cream.