Peel and core apples then place into a large bowl. Using a spatula, stir in few drops of lemon juice to prevent browning.
Preheat oven to 425 degrees Fahrenheit.
Melt butter in a sauce pan. Stir in flour. Add water, sugar, brown sugar and cinnamon and bring to a boil. Reduce heat and let simmer.
Unroll out a prepared pie shell and place into a pie pan. Crimp edges to seal. Add prepared apples to pan, then pour the butter mixture on top.
Unroll the second prepared pie shell and place on top of pie. Crimp outer edges on dough to seal in the filling. Trim off any excess. With a knife, add 4 to 6 slits to vent steam when baking.
In a small bowl, separate egg whites and discard yolk. Whisk whites then brush the crust lightly to coat.
Bake 15 minutes at 425 degrees, then reduce heat to 350 degrees and continue to bake for 35-45 minutes until apples are soft. Use aluminum foil to cover edges if they brown too quickly.
Remove from oven and let cool, or if serving warm, allow to rest for about 10 minutes before cutting. Serve with a scoop of vanilla bean ice cream on top. Enjoy!