Step 1: In a large bowl, whisk together the flour, 1 teaspoon salt, and 1 tablespoon granulated sugar. Add the very cold, cubed butter. Using a pastry blender, your fingertips, or a food processor, cut the butter into the flour mixture until it resembles coarse crumbs with some pea-sized pieces of butter remaining. This texture is crucial for a flaky crust.
Step 2: Gradually add 1/2 cup ice water, one tablespoon at a time, mixing gently until the dough just comes together. Do not overmix. Gather the dough into two balls, flatten slightly into discs, wrap tightly in plastic, and chill in the refrigerator for at least 30 minutes, or up to 2 days.
Step 3: On a lightly floured surface, roll out one disc of dough into a 12-inch circle. Carefully transfer it to a 9-inch pie plate. Trim the edges, leaving about a 1/2-inch overhang. Place in the fridge while you prepare the filling.
Step 4: In a large bowl, combine the peeled, cored, and sliced apples. Add 1/2 cup granulated sugar, the brown sugar, cinnamon, nutmeg, a pinch of salt, and the lemon juice. Toss gently to coat the apples evenly. For a thicker filling, you can also add 1-2 tablespoons of cornstarch or flour here.
Step 5: Pour the apple filling into the chilled pie crust, mounding the apples slightly in the center. Dot the top of the filling with the small pieces of butter.
Step 6: Roll out the second disc of dough into a 12-inch circle. You can either place it whole over the filling (cutting a few slits for steam to escape) or cut it into strips to create a beautiful lattice top.
Step 7: Trim the edges of the top crust, leaving a 1/2-inch overhang. Fold the top crust overhang under the bottom crust overhang and crimp the edges together to seal. Brush the top with the egg wash and sprinkle with 1 tablespoon granulated sugar.
Step 8: Place the pie on a baking sheet and bake in a preheated oven at 425°F (220°C) for 15 minutes. Then, reduce the oven temperature to 375°F (190°C) and continue baking for another 45-60 minutes, or until the crust is golden brown and the filling is bubbly. If the crust browns too quickly, loosely tent it with aluminum foil.
Step 9: Allow the apple pie to cool completely on a wire rack for at least 2-3 hours before slicing and serving. This cooling allows the filling to set properly, preventing it from being too runny.