Add the flour, granulated sugar, and salt to a food processor and pulse two or three times to combine. Scatter the cold butter cubes over the top and pulse in short bursts until the mixture looks like coarse crumbs with some pea-sized pieces of butter still visible.
Drizzle in 6 tablespoons of ice water and pulse just until the dough starts to clump. Add the remaining water 1 tablespoon at a time only if it looks dry. Turn the dough out and divide it in half.
Shape each half into a flat disk, wrap in plastic, and refrigerate for at least 1 hour.
Peel, core, and slice the apples 1/4 inch thick, then toss them in a large bowl with the lemon juice. In a small bowl, stir together the granulated sugar, brown sugar, cornstarch, cinnamon, nutmeg, and salt.
Sprinkle the sugar mixture over the apples and toss until every slice is coated. Transfer everything to a saucepan or skillet, add the 2 tablespoons of butter pieces, and cook over medium heat, stirring often, for about 5 minutes.
Remove from the heat and let the filling cool while you roll the crust. Warm filling melts the butter in the dough, so this step matters.
On a lightly floured surface, roll one dough disk into a 12-inch circle about 1/8 inch thick. Drape it over your rolling pin and lift it into a 9-inch pie dish, easing it gently into the corners without stretching.
Trim the overhang to about 1/2 inch and slide the lined dish into the refrigerator while you roll the top.
Roll the second disk into another 12-inch circle. For a lattice, cut it into strips about 3/4 inch wide. Spoon the cooled filling into the chilled bottom crust, mounding it slightly in the center and leaving any excess liquid behind in the pan.
Lay the top crust over the filling, or weave the strips into a lattice. Trim the top crust to match the bottom, then fold the two edges together and crimp to seal. Sealing well keeps juices from bubbling out.
If you used a solid top crust, cut four or five 1-inch vents in the center so steam can escape. Brush the whole surface with the beaten egg wash, then sprinkle evenly with the coarse turbinado sugar.
Place the pie in the refrigerator for 15 minutes while the oven heats. A cold pie going into a hot oven holds its shape far better.
Preheat the oven to 425°F (220°C) with a rack in the lower third and a rimmed baking sheet on it. Set the pie on the hot baking sheet and bake at 425°F (220°C) for 20 minutes to set the bottom crust.
Reduce the heat to 375°F (190°C) and bake for another 35 minutes, until the crust is deep golden and the filling bubbles slowly through the vents. Shield the edges with foil if they darken too fast.
Move the pie to a wire rack and let it cool for at least 2 hours before slicing. This wait lets the filling finish thickening, which is the difference between neat slices and a runny plate.