Preheat oven to 350º
Peel apples, and cut into 1/2-inch-thick wedges
Toss apples with cinnamon and 3/4 cup granulated sugar
Melt butter in a 10-inch cast-iron skillet over medium heat; add brown sugar, and cook, stirring constantly until sugar is dissolved
Remove the skillet from the heat and place 1 pie crust in the skillet over the brown sugar mixture
Spoon apple mixture over the pie crust, then top with the remaining pie crust
Whisk the egg white until foamy then brush the top of the pie crust with the egg white and sprinkle the top with 1 tablespoon of granulated sugar
Cut a few slits into the top of the pie for steam to escape
Bake the pie at 350º for approximately 1 hour or until the pie is golden brown and bubbly
Cool on a wire rack 30 minutes before serving
Serve with vanilla ice cream