Preheat oven to 350℉.
Peel apples, and cut into 1/2-inch thick wedges. Toss apples with cinnamon and 3/4 c. granulated sugar.
Melt butter in a 10-inch cast-iron skillet over medium heat; add brown sugar, and cook stirring constantly, 1 to 2 minutes or until sugar is dissolved. Remove from heat, and place 1 pie crust in skillet over brown sugar mixture.
Spoon apple mixture over pie crust, and top with remaining pie crust.
Whisk egg white until foamy. Brush top of pie crust with egg white; sprinkle with 2 tbsp. granulated sugar. Cut 4 or 5 slits in top for steam to escape.
Bake at 350℉ for 1 hour to 1 hour 10 minutes or until golden brown and bubbly, shielding with aluminum foil during last 10 minutes to prevent excessive browning, if necessary.
Cool on a wire rack 30 minutes before serving.
