Combine flour and salt in a large bowl. Add cold, cubed butter and use your hands or a pastry cutter to work it into the flour until the mixture looks like coarse crumbs.
Slowly drizzle in ice-cold water, a tablespoon at a time, mixing until the dough comes together.
Shape into two balls, wrap in plastic, and refrigerate for at least 30 minutes.
While the dough chills, peel, core, and slice the apples. Toss them with lemon juice to keep them fresh.
In a separate bowl, stir together the sugars, flour, cinnamon, nutmeg, ginger, and salt. Then, combine this mixture with the apples, ensuring every slice is well coated.
Take one dough ball from the fridge and let it rest for a few minutes. On a lightly floured surface, roll it into a circle large enough to fit a 9-inch pie pan. Gently transfer to the dish, pressing it into the bottom and sides.
Pour the apple mixture into the crust, mounding slightly in the center. Dot with small cubes of butter.
Roll out the second dough ball into a slightly larger circle and place it over the apples. Trim excess dough, fold edges under, and crimp to seal. Cut a few slits in the top for steam to escape.
Brush the crust with beaten egg, then sprinkle with sugar.
Place the pie on the middle rack of a preheated oven at 400°F. Bake for 45–50 minutes, until the crust is golden and the filling is bubbling.
Let the pie cool on a wire rack for at least 2 hours before slicing. Enjoy!