
Prepare the dough: Combine the flour, butter, sugar and salt in the bowl of a food processor and pulse until pea-size clumps form. Add the water and pulse a few times to help the dough come together. It should start to form clumps. (Alternatively, prepare dough without a food processor: Combine the flour, butter, sugar and salt in a large mixing bowl and toss to coat the butter with flour. With your hands, pinch the butter into the dough to form pea-size pieces in the flour mixture. Drizzle in ice water and, with your hands or a wooden spoon, mix to combine.)
Divide the dough evenly between two pieces of plastic wrap. Wrap tightly, flatten into disks and refrigerate the dough for at least 4 hours or preferably overnight.
Make the filling: Melt the butter in a large saucepan over medium heat. Once the butter is foamy, add the apple slices and salt, and cook, stirring occasionally, until the apples are softened and lightly translucent on the edges, 10 to 12 minutes. Scrape the apples into a large mixing bowl and cool at room temperature, about 30 minutes. (You can prepare the apples ahead of time and chill them in the refrigerator until you’re ready to bake the pie. They’ll hold for up to 48 hours.)
While the apple slices are cooling, take the pie dough from the refrigerator and let sit at room temperature for 10 to 15 minutes to soften slightly. Roll one disk of dough on a lightly floured surface into a 12-inch circle, then transfer to a 9-inch pie plate. Gently press to adhere and tuck in any excess dough that overhangs the edges.
Stir the sugars, cornstarch, cinnamon, nutmeg and heavy cream into the cooled pie filling and scrape into the prepared crust. Place into the fridge while you work on the top crust.
Roll the other disk of dough into a 12-inch square, then use a knife or pizza cutter to cut the dough into 16 (3-inch) squares. Don’t worry if the squares are not precise. Shingle the squares, slightly overlapping, onto the apples to cover. There’s no need to crimp the crust or press the squares to seal. Place the pie in the refrigerator and chill for about 30 minutes.
While the pie chills, arrange a rack in the middle of the oven, and heat the oven to 375 degrees. Line a baking sheet with foil and place in the oven while it heats.
Make the egg wash: Whisk together the egg and heavy cream, and brush the top of the pie all over with the egg wash. Sprinkle the sugar in an even layer. Place the pie on top of the hot baking sheet and bake until it is deeply golden brown on top, rotating halfway through, 80 to 90 minutes. Remove the pie from the oven and cool at least 1 hour before serving.