Using a food processor, pulse the flour, sugar, and salt together to combine.

Scatter the shortening over the top of the dry products, then using about 10 one-second pulses, process until mixture looks like coarse sand.

Scatter the butter over the mixture, pulse for one-second about 10 times, until mixture looks like coarse crumbs. Butter and shortening bits should be no bigger than small peas.

Place mixture into a medium bowl. Sprinkle 6 tablespoons of the ice water over the mixture, then use a rubber spatula to fold the water into the other ingredients.

Press down with the flat side of the spatula on the dough so the dough sticks together. If necessary (it wasn't for me), add up to 2 more tablespoons of the ice water.

Divide the dough into 2 balls, flatten into 4-inch disks, wrap in plastic wrap, and refrigerate for at least one hour or up to two days.

Peel and core your apples, then slice into even slices about ⅛" thick, using either a food processor with the standard 3mm slicing blade (thinnest attachment), mandoline, or sharp knife.

In a Dutch oven, toss the apples with the sugars, lemon zest, salt, cinnamon, and optionally (I did accidentally) 2 teaspoons of lemon juice. Place on the stove over medium heat, cover, and cook for 15-20 minutes, stirring occasionally, until tender but not falling apart.

Transfer the apples and their juices to a rimmed baking sheet. Let cool to room temperature, at least 30 minutes.

Meanwhile, roll out one disk of your refrigerated dough into a 12-inch circle on a lightly floured large work surface.

Gently fit into a 9-inch pie plate, letting the excess hang over the edge. Cover with plastic wrap and refrigerate for 30 minutes.*

Roll out the other dough disk, again into a 12-inch circle on a lightly floured work surface. Place this dough circle on a baking sheet lined with parchment paper, cover the dough with plastic wrap, and refrigerate for 30 minutes.*

Move an oven rack to the lowest or second-lowest position in your oven. Place a rimmed baking sheet on that rack**, and heat the oven to 425.

Drain the cooled apples into a colander, catching the reserved juices in a bowl. Reserve ¼ cup of the juice and stir in 2 teaspoons lemon juice. (I had only ⅕ cup of juice left from the apples cooking, and my pie turned out fine.)

Evenly spread the apples across the dough-lined pie dish.***{See Notes for variations here} Mound apples slightly in the middle, then drizzle with the apple-lemon juice.

Use a rolling pin to pick up the second piece of pie dough by gently rolling the dough around the pin. Unroll the dough over the filled pie dish. Trim the edges so only ½" of dough remains overhanging the dish. Press the top and bottom crust together, then tuck underneath. Crimp the dough evenly around the pie dish, using your fingers to form the crimp pattern. Slash the top pie dough four times to create vents in the top (see pictures).

Brush the crust with the beaten egg white, then sprinkle with the one tablespoon of sugar.

Place the pie in the 425 F oven on the heated baking sheet. Cook for 25 minutes, until crust is golden.

Rotate the baking sheet, reduce the oven temperature to 375 F, and continue baking another 25-30 minutes longer, until the juices are visibly bubbling and the top is deeply golden. If the pie is browning too quickly, cover with foil.

Place pie on a wire rack and let cool until the filling sets completely, about 2 hours.

Serve warm or at room temperature (honestly, it's even delicious cold), ideally with vanilla bean ice cream.

This pie will keep for 3 days tightly-wrapped in the refrigerator. It can also be frozen and gently reheated for longer periods of storage (up to one month).