01 - In a large bowl, whisk together flour, salt, and sugar. Using a pastry cutter or fork, cut in the cold butter until the mixture forms coarse crumbs.
02 - Add ice water, one tablespoon at a time, mixing until dough just comes together. Divide the dough in half, shape into discs, wrap in plastic, and refrigerate for a minimum of one hour.
03 - In a separate bowl, toss sliced apples with granulated sugar, brown sugar, flour, cinnamon, nutmeg, lemon juice, and vanilla extract until evenly coated. Set aside.
04 - Preheat oven to 400°F. Roll out one dough disc on a floured surface to fit a 9-inch pie dish. Place dough in dish and add the apple filling.
05 - Roll out the second dough disc and place over the apples. Trim and crimp the edges. Cut slits or create a lattice to allow steam to escape. Brush the surface with beaten egg and sprinkle with coarse sugar if desired.
06 - Set pie on a baking sheet and bake for 45 to 55 minutes, until the crust is golden brown and filling is bubbling. Protect the edges with foil midway if browning quickly.
07 - Let the pie cool for at least 2 hours before slicing to allow the filling to set.