Preheat the oven to 425 degrees. (You are starting the oven temperature at 425, but will lower it to 350 after it cooks 10 minutes).
Place a pie crust in a 9-inch pie pan.
In a large bowl, add the sliced apples, cinnamon, white and brown sugar, flour, and lemon juice and toss until combined and covering all of the apple slices.
Next, pour apple mixture into the pie crust.
Place the cubed butter all over the pie.
Top with the second pie crust and pinch the edges together. Cut out two or three small slits in the pie for the steam to escape.
In a small bowl, mix the egg white and water and brush on top of the pie.
Sprinkle with a handful of cinnamon and sugar.
Bake pie at 425 for 10 minutes. Then, reduce the heat to 350 degrees and continue baking for about 35 to 40 minutes or until the top is golden brown.
Let the pie rest for two hours at room temperature before cutting into it.