In a large mixing bowl, whisk together the flour, salt, and sugar.
Add the cold, cubed butter to the bowl. Use a pastry cutter or your fingers to cut the butter into the flour mixture until it resembles coarse crumbs.
Gradually add the ice water, one tablespoon at a time, mixing until the dough just comes together. Do not overmix.
Divide the dough into two equal parts, shape them into discs, wrap them in plastic wrap, and refrigerate for at least 1 hour.
In a large mixing bowl, combine the sliced apples, granulated sugar, brown sugar, cinnamon, nutmeg, allspice, flour, lemon juice, and vanilla extract. Toss to coat the apples evenly. Set aside.
Preheat your oven to 425°F (220°C).
On a lightly floured surface, roll out one disc of dough to fit a 9-inch (23 cm) pie dish, leaving an overhang. Transfer the rolled dough to the pie dish.
Pour the apple filling into the crust, mounding it slightly in the center.
Roll out the second disc of dough and place it over the apples. Trim any excess dough, then crimp the edges to seal.
Cut a few small slits in the top crust to allow steam to escape.
Brush the top crust with the beaten egg and sprinkle with granulated sugar.
Place the pie on a baking sheet to catch any drips.
Bake in the preheated oven for 45-55 minutes, or until the crust is golden brown and the filling is bubbling.
If the edges of the crust start to brown too quickly, cover them with aluminum foil.
Allow the pie to cool on a wire rack for at least 2 hours before serving to let the filling set.
Enjoy your meal!