In a large bowl, whisk together flour, sugar, and salt, then cut in the very cold butter until the mixture resembles coarse crumbs with pea-sized pieces of butter remaining.

Gradually add ice water, mixing until a dough forms, then divide the dough in half, flatten into discs, wrap, and chill for at least 30 minutes.

In a large bowl, combine sliced apples with granulated sugar, brown sugar, flour, cinnamon, nutmeg, and lemon juice, tossing gently to coat evenly.

Set aside the apple mixture while you prepare the crust.

On a lightly floured surface, roll out one disc of chilled dough into a 12-inch circle and carefully transfer it to a 9-inch pie plate.

Pour the apple filling into the pie crust, dot with small pieces of butter, and roll out the second dough disc for the top crust or lattice, placing it over the apples.

Trim and crimp the edges of the crust to seal, cut several slits in the top crust for steam to escape, then brush with beaten egg and sprinkle with sugar.

Chill the assembled pie in the refrigerator for 15-20 minutes before baking.

Preheat your oven to 425°F (220°C) and place the pie on a baking sheet to catch any drips.

Bake for 15 minutes, then reduce the oven temperature to 375°F (190°C) and continue baking for another 35-45 minutes, or until the crust is golden brown and the filling is bubbly.

If the crust browns too quickly, cover the edges with aluminum foil.

Let the pie cool completely on a wire rack for at least 2-3 hours before slicing and serving, allowing the filling to set properly.