Preheat the oven to 450°F (230°C).
Line a 9-inch pie dish with one pastry crust and set the second crust aside.
In a small bowl, mix sugar and cinnamon. Add extra sugar if your apples are tart.
Layer the apple slices in the pie crust, sprinkling each layer with the cinnamon-sugar mixture.
Dot the top layer with small pieces of butter.
Cover with the second crust, sealing the edges by fluting them.
Beat the egg with 1 tablespoon of water to make an egg wash, then brush it over the top crust.
Cut slits on top to allow steam to escape.
Bake on the lowest rack for 10 minutes. Reduce the oven temperature to 350°F (175°C) and bake for another 30–35 minutes until golden and bubbly.
Let cool slightly before serving warm or cold.