For the crust: Put the flour, sugar and salt into the bowl of a food processor fitted with the pastry blade and pulse a few times to combine. Add the butter and pulse a few times until the mixture resembles fine gravel. Add 1/4 cup ice water a few tablespoons at a time until the dough comes together and forms a ball. Remove from the food processor, divide in two and form each piece into a disk. Wrap in plastic wrap and refrigerate for at least 30 minutes or until ready to use.
For the filling: In a large bowl, combine the apples, sugar, cornstarch, crystallized ginger, cinnamon, lemon juice, vanilla bean paste and salt.
Preheat the oven to 425 degrees F and remove one of the disks of dough from the refrigerator. If necessary, leave to soften for 10 minutes or so. On a floured surface, roll out the disk into a 12-inch round about 1/8-inch thick. Transfer to a 9-inch pie dish and gently press into place, eliminating any air pockets. Trim the dough overhang to 1/2 inch.
On a floured surface, roll the second disk into a 12-inch round about 1/8-inch thick. Transfer the apple filling to the dough-lined dish. On top of the filling, add the second crust, allowing each to overhang by 1/2 inch. Fold the top crust edges over the overhang of the bottom crust and crimp the edges to seal. Cut six slits into the top crust.
Beat the egg with 1 to 2 tablespoons of water. Using a pastry brush, lightly paint the crust with the egg. Using aluminum foil, make a "collar" around the edges of the pie to prevent it from browning too quickly.
Bake 15 minutes. Reduce the oven temperature to 350 degrees F and continue baking until the crust is golden brown and the filling is bubbly, about 1 hour. (Remove the foil collar for the last 10 to 15 minutes.)
Transfer the pie to a rack and cool completely.
Serve with a scoop of vanilla ice cream.