Heat oven to 350. Peel and cut apples into wedges. Mix with cinnamon and 3/4 cup graulated sugar.
Add butter to skillet and cook over medium heat. Add brown sugar, and cook stirring constantly for 1-2 minutes (until sugar dissolves.)
Remove skillet from heat and place one of the pie crusts on top of the brown sugar mixture. Then add the apple/cinnamon sugar mixture, and top with the second crust.
Whisk egg white until fluffy, and brush the top of the pie crust with the egg white.
Sprinkle 2 tablespoons of sugar onto pie crust.
Cut a few slits in top of pie crust to vent.
Bake at 350 for between 1 hour and 1 hour and 10 minutes (mine was done at 1 hour.) During last ten minutes you may need to cover the pie with foil to keep the pie from browning too much. (Mine was fine without covering, be sure to watch it as you don't want your crust to burn.)
Cool on wire rack for at least thirty minutes, and serve with ice cream.