Peel, core and slice the apples.
Toss all of the apples with 1/4 cup of the sugar.
Pour the apples in a colander set over a large bowl and allow to drain for 1 1/2 hours.
While the apples are setting prepare your pie dough and let it set in the fridge for a hour.
Adjust an oven rack to the lowest position and place a rimmed baking sheet on the rack.
Heat the oven to 500 degrees.
In a large bowl, toss the apples with the remainder of sugar, brown sugar, flour, lemon juice, sea salt, nutmeg, and cinnamon. Set mixture aside.
Roll out the double pie crust on a floured surface then place the bottom crust in the pie pan.
Pour the apple mixture into the pie crust, than top with the top pie crust. Crimp the edges of the crust using your fingers.
Cut 4-5 vent holes in the top of the pie crust. Brush the top crust with the beaten egg white, and then sprinkle the sugar in the raw on top.
Place the pie on the hot baking sheet in the oven then reduce the temperature to 425 degrees.
Bake until the top crust is golden brown, this should take 20-25 minutes.
Once the top is golden brown, rotate the baking sheet, and turn the temperature down to 375 degrees. Bake another 30-35 minutes, until the top crust is a deep golden brown.
Remove the pie from the oven and allow it to cool before serving.
Top with a big scoop of vanilla ice cream for an extra treat.