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.