Pulse flour, sugar, and salt in a food processor to combine. Add Le Gruyère AOP and pulse a few more times. Add the butter and pulse until the mixture resembles coarse cornmeal with a few larger pieces scattered around.
With the machine running, pour in the ice water until just combined, then turn the machine off. The dough should look like it’s barely formed. Turn the mixture out into a large bowl and knead a few times by hand until it forms a large ball. Do not overwork.
Divide the dough in half and press into two discs, and wrap tightly in plastic wrap. Chill for at least 1 hour.
Prepare Filling:
In a large bowl, whisk together the sugars, cinnamon, allspice, nutmeg, salt, and cornstarch. Add the apples and toss to evenly combine.
In a Dutch oven or large saucepan set over medium heat, melt the butter, allowing it to brown slightly. Add the apple mixture, stirring to coat with the butter. Cover the pan and cook for 7-8 minutes, stirring once or twice to make sure nothing is sticking. Remove the cover and continue cooking for an additional 3-5 minutes on medium or medium-high heat to slightly thicken and reduce the juices.
Remove from heat and cool filling completely, at least 1 hour. You can speed up this process by transferring the filling to a clean bowl and placing it in the refrigerator.
Assemble Pie:
Place an oven rack on the lower third shelf and preheat the oven to 400 degrees F. Let one of the dough discs sit at room temperature for a few minutes to slightly soften the butter, then roll out on a lightly floured surface until it will fit in a 9x2 inch pie dish with slight overhang. (This can be done while the filling cools; place the pie dish in the refrigerator after it’s rolled out to keep the dough chilled.)
Roll out the second section of pie dough so that it will fit over the top of the 9-inch pie dish with a slight overhang. (Again, this can be done while the filling cools. Place the rolled dough on a large cutting board and place in the refrigerator until needed).
Once the pie filling is at room temperature or colder, add to the pie dish evenly, making sure there’s not much space in between the apples if they’re cut in larger pieces (thinner slices will lay more flat). Top with the second layer of crust, trimming away excess dough and crimping the edges together. Chill for 10 minutes.
Place the pie on a baking sheet. Use a small knife to make 5 2-inch steam vents in the top of the dough. Lightly brush egg wash all over the top of the pie and sprinkle with turbinado sugar.
Bake for 15 minutes, then reduce the temperature to 350 degrees and bake for an additional 35-50 minutes, until the top is a deep golden brown. Cover top with foil to keep from browning too quickly, if necessary. Because this dough includes cheese, it will develop a slightly darker color than typical pie crust.
Cool completely before slicing. Serve with thinly shaved fresh gruyere (I used a vegetable peeler).
Store any leftover pie, lightly covered, at room temperature for several days. Freeze for longer storage.
Notes
To save time, I recommend using an Apple Peeler & Corer. Not only does it peel, core and slice the apples quickly, but it cuts the slices thinly so that they lay flat in the pie.
You can make this pie dough up to 24 hours in advance, but no more or it will begin to oxidize. For a more pronounced gruyere flavor in the crust, you can go up to 4 ounces of cheese in the pie dough. However, I recommend sticking with 3 ounces and serving with slices. You still get the gruyere flavor in the crust (mostly up front and at the end), but it’s less likely to bother pie traditionalists.