Line a baking sheet with parchment paper and place on the bottom rack of the oven. Heat oven to 450°F.
On a lightly floured surface, roll 1 disk of dough into a 11 to 12-inch circle (about 1/8-inch thick), and place in a 9-inch deep-dish pie plate. Press into plate so the dough is snug against the edge.
Give filling a few more stirs to distribute all the juices and pour into pie shell. Press down on the filling so the apples are compact.
Roll out remaining disk of dough the same as the first and lay over filling. Pinch the two edges of dough together and trim off any that hangs over the lip of the plate by more than 1 inch.
Make a decorative edge by pinching sections of dough around the pointer finger of one hand with the thumb and pointer finger of the other, making little triangles as you go around the perimeter of the pie.
With a sharp knife, make a few slits on the top of the pie to let steam escape. Place in the freezer for 15-30 minutes before baking to make sure the pie dough holds its shape.
Beat egg with a teaspoon of water and brush egg wash over the top of the pie. Sprinkle top with sugar and place on heated baking sheet in the oven. Bake until just starting to turn golden, about 15 minutes, then reduce heat to 350°F. Continue baking until crust is a deep golden brown and filling is bubbling in the middle, about 45 minutes more. Remove from oven and let cool at least 1 hour before serving.