Peel, core and slice the apples. Place them in a bowl with sugar, cinnamon, lemon juice and cornstarch. Stir to combine. Let sit until ready to fill the pie dish.
Preheat the oven to 400°F.
On a floured work surface, roll out the first disk to about ¼ inch thick. You may need to let it sit out at room temperature for a couple minutes to be able to roll it.
Place the dough into a 9 inch pie dish and press the edges into the edges of the dish. There should be some dough hanging over the edges.
Fill the crust with the apples, ensuring the apples fill all the way up to the rim of the dish, even forming a mound.
Roll the second disk to the same thickness. Cut into strips. Create a lattice over the apples and use the overhanging dough to seal the edges.
In a small bowl, beat the egg and water for the egg wash. Brush evenly over the lattice strips.
Bake for about an hour total, until the crust is golden brown. After about 20 minutes in the oven, it may be necessary to cover the top with a piece of foil to prevent it from burning.
Let cool for at least 1 hour.