Prepare the Crust: In a food processor, combine the flour, salt, and sugar. Pulse to mix. Add the cold butter and pulse 6–8 times until the mixture resembles coarse crumbs. Gradually add cold water, one tablespoon at a time, until the dough starts to clump together.
Chill the Dough: Divide the dough into two equal portions and gently shape each into a disk without over-kneading. Wrap each disk in plastic wrap and refrigerate for at least 1 hour, or ideally overnight.
Preheat the Oven: Preheat your oven to 200°C.
Form the Crust: Take one chilled dough disk and let it sit at room temperature for 5 minutes. Roll it out on a lightly floured surface into a 12–13-inch round, about 1⁄8 inch thick. Carefully transfer the dough to a 9-inch pie plate, pressing it down to line the bottom and sides of the tin. Trim any excess dough.
Prepare the Filling: In a large bowl, combine the sliced green apples, granulated sugar, cornstarch, vanilla essence, lemon juice, and ground cinnamon. Toss to coat. Pour the filling evenly into the pie dish.
Create the Top Crust: Remove the second chilled dough disk from the refrigerator and roll it into a 12-inch diameter circle. Cut 10 1.5-inch-wide strips using a pastry wheel, sharp knife, or pizza cutter.
Assemble and Bake: Weave the strips over and under each other on top of the filling, pressing the edges into the bottom crust to seal. Trim any excess dough.
Prepare the Egg wash: In a small bowl, prepare the egg wash by whisking together one egg with a tablespoon of water. Lightly brush the top of the pie crust with the egg wash and sprinkle it with demerara sugar.
Baking: Bake at 200°C for 15 minutes. Then, reduce the heat to 180°C and continue baking for another 45 minutes. In the last 15 minutes of baking, cover the edges of the pie pan with aluminum foil to prevent over-browning.
Serve: Allow the pie to cool for at least 2 hours before serving, but for the best results, let it chill overnight. Enjoy your delicious homemade apple pie!