In the bowl of a food processor, pulse together the flour, sugar, and salt until combined. Add the shortening and pulse until pea-sized crumbs form. Transfer the dough to a large bowl and bring the dough together with a wooden spoon.
In a small bowl, whisk together the egg, vinegar, and water. Pour over the dough and mix until combined (dough will be sticky). Cover with plastic wrap and chill in the refrigerator for at least 1 hour before rolling.
After the hour, remove the dough from the refrigerator and unwrap it. Split the dough into two equal halves and let it sit for about 15 minutes as you prepare the apples.
Preheat the oven to 425°F and place the oven rack into its lowest position.
Place the sliced apples in a large bowl. In a medium bowl, combine the sugar, flour, cinnamon, and kosher salt.
Add the sugar mixture to the bowl of apples and toss to coat. Set aside as you roll the dough.
On a lightly floured surface, roll each of your dough sections into 12-inch circles.
Carefully add one of the crusts to a 9-inch, deep-dish pie plate.
Spoon the apple mixture into the prepared crust, and top with the butter pieces.
Place the other pie crust over the top of the filled pie pan and press down to crimp the edges. Use a sharp knife to cut small slits in the pie crust for venting.
In a small bowl, mix together the egg and water for an egg wash. Brush this over the pie crust.
Bake for 15 minutes. Then, reduce the oven temperature to 350°F, cover the pie loosely with aluminum foil, and bake an additional 45-50 minutes. The pie is done when the crust is golden brown and the apples are tender.
Let the pie cool at least an hour before serving.