Preheat the oven at 400° F.
In a large, heavy-bottomed saucepan, melt butter over medium heat. Stir in apples, lemon juice, 1/2 cup sugar, 1/4 cup brown sugar, 1/2 teaspoon cinnamon, and salt. Cover and cook until apples have softened but are not falling apart, about 8 minutes. Add flour and cook, uncovered, until juices have thickened, about 2 minutes. Transfer to a 9-by-13-inch baking dish; let cool.
Grease a glass pie dish. Starting from the middle and working your way outwards, gently pat down one of your store-bought pie crusts so that it lies flat on the plate. (Leave your second crust in the fridge for now.) Use a fork to make 7-10 indentations in the bottom of the crust to prevent bubbles from forming.
Line the crust with a piece of aluminum foil and fill the foil with dried rice or beans. (Or you can invest in pie weights, small ceramic balls that keep a pie crust from bubbling and shrinking away from the edge of the dish.)
Blind bake for 15 minutes.
Meanwhile, remove your 2nd pie crust from the fridge and lay flat onto a baking sheet or parchment paper. Using a small paring knife, cut a 1-inch hole in the center. Brush top with egg white and refrigerate until firm, about 20-30 minutes.
Remove your blind-baked crust from the oven and fill with apple mixture.; spread in an even layer. in the interest of keeping a flat surface, I wound up using slightly less than the full mixture. lightly brush rim of bottom crust with water.
In a small bowl, combine remaining 1/2 teaspoon cinnamon and 1 tablespoon sugar.
Remove your top dough from the fridge and lay it over your blind-baked pie. Center your parchment paper collar over your top dough. Place 4 popsicle sticks around center hole, at 90-degree angles. Starting at center and working outward, place sticks 1/2 inch apart, gently pressing to the dough to adhere, to create an arrow pattern toward center of dough.
Using a small sieve, sprinkle with cinnamon sugar mixture.Brush excess off sticks; carefully remove sticks, then parchment collar.
Trim dough, leaving a 1-inch overhang. Tuck overhang under edge of bottom dough, gently pinching to seal. Crimp as desired.
Bake at 400°F for about 20 minutes, until the crust is set and just beginning to take on color. Reduce oven temperature to 375° F and bake until crust is golden brown and juices are bubbling in the center, about 30-40 minutes. If crust is growing too quickly, tent with foil.
Transfer to a wire rack. Let cool completely.