For the crust:
For the filling:
For the topping:
In a large mixing bowl, whisk together the flour, sugar, and salt.
Add the cubed butter to the bowl and use a pastry cutter or your fingers to work the butter into the flour mixture until it resembles coarse crumbs.
Gradually add the ice water, one tablespoon at a time, and stir the mixture until it comes together into a ball of dough.
Divide the dough in half and shape each half into a flat disc. Wrap each disc in plastic wrap and refrigerate for at least 30 minutes.
Preheat your oven to 375°F (190°C).
In a large mixing bowl, combine the sliced apples, lemon juice, granulated sugar, brown sugar, cinnamon, nutmeg, and salt. Stir until the apples are evenly coated.
On a lightly floured surface, roll out one disc of the chilled dough into a large circle that's about 12 inches in diameter. Transfer the dough to a 9-inch pie dish and trim any excess dough from the edges.
Pour the apple filling into the pie crust and dot the top with the cubed butter.
Roll out the second disc of chilled dough into another large circle that's about 12 inches in diameter. Cut the dough into thin strips and use them to create a lattice pattern on top of the apple filling.
Brush the beaten egg over the top of the pie and sprinkle with the granulated sugar.
Bake the pie in the preheated oven for 45-50 minutes, or until the crust is golden brown and the filling is bubbling.
Let the pie cool for at least 30 minutes before slicing and serving.
Enjoy your delicious homemade apple pie!