Preheat the oven to 375° F (190° C).
On a floured surface, roll out your pie dough to about 12-14 inches. Transfer to a parchment-lined baking sheet and set aside.
Peel and core your apples and then cut them into bite-size chunks. Add them to a large mixing bowl.
To the bowl of apples, add the granulated sugar, brown sugar, flour, and cinnamon. Give it a good mix to coat the apples.
Grab your baking sheet with the pie dough and pile the apple mixture in the center of the pie dough, leaving a 2-inch border all around. Do not add any apple juices that may have accumulated at the bottom of the bowl.
Brush the beaten egg on the dough border and then fold the dough over the outside edges of the apples, overlapping the dough every so often.
Now brush the top of the folded dough crust with the egg and sprinkle on a little bit of the optional turbinado sugar all over the crust.
Add the butter cubes on top of the exposed apple pieces.
Bake for 45-50 minutes or until the apples are soft and tender and the crust is golden brown. Let it cool for 10 minutes before serving.