In a large mixing bowl, combine the sliced apples, vanilla extract, white sugar, brown sugar, flour, cornstarch, cinnamon, nutmeg, and salt. Toss the mixture thoroughly until the apples are evenly coated. Set aside while preparing the crust.

Preheat the oven to 425°F (220°C).

In the bowl of a food processor, combine the flour and salt. Add the cold cubed butter and pulse until the mixture resembles a coarse meal.

Add 8 tablespoons of ice-cold water and pulse several times until the dough begins to clump together. If the dough remains too dry, add additional water, 1 tablespoon at a time, pulsing briefly after each addition.

Turn the dough out onto a lightly floured surface and divide it in half. Shape each half into a ball, then flatten each into a disk. Wrap the disks in plastic wrap and refrigerate them while preparing the pie plate and filling.

Using a lightly floured rolling pin, roll out the first dough disk until it is slightly larger than the pie dish. Carefully transfer the dough to the pie plate and trim any excess. Add the apple filling evenly into the crust.

Roll out the second dough disk using the same method as the first.

For a full top crust, place the second crust over the filling, trim any excess dough, and press the edges together to seal. Crimp the edges as desired and cut several slits in the top to allow steam to escape.

For a lattice top crust, cut the rolled dough into evenly sized strips using a knife or pizza cutter. Arrange the strips in a lattice pattern over the filling. Trim the excess dough and fold the edges inward, pinching gently to seal. Crimp the edges if desired.

Place the assembled pie in the refrigerator for approximately 10 minutes. This helps ensure the crust remains cold before baking.

In a small bowl, whisk together the egg and water until fully combined. Remove the pie from the refrigerator and brush the top crust evenly with the egg wash.

Bake the pie at 425°F for 15 minutes.

Then reduce the oven temperature to 350°F (175°C) and continue baking for 40 to 50 minutes, or until the crust is golden brown and the filling is bubbling.

If the crust begins browning too quickly, loosely tent the pie with aluminum foil to prevent over-browning.

Remove the pie from the oven and allow it to cool slightly before slicing. This helps the filling set properly.

Serve warm or at room temperature, optionally with vanilla ice cream.