Mixing the flours and butter. Using a stand mixer (or a food processor), combine all the dry ingredients. Cut the butter into little pieces, about 1/2 inch thick, and drop the pieces into the dry ingredients. Turn on the mixer again and mix on low speed until the butter has crumbled into pea-size pieces.
Adding the wet ingredients. Drop in the egg and apple cider vinegar as the mixer is running. Once they are incorporated, slowly drizzle the ice-cold water into the mixture, a little at a time, while the mixer is running. When the mixture coheres and looks like dough, turn off the mixer.
Refrigerating the dough. At this point, drop the ball of dough onto a large piece of parchment paper. (Prepare this ahead, unless you want to wipe dough off the box of parchment paper later!) Place another piece of parchment paper, the same size, on top of the dough. Gently, smoosh the dough outward, equally in all directions, until it is a thick, round cake of dough. Refrigerate the dough for as long as you can. Ideally, you should prepare the dough in the evening and refrigerate overnight. Take the dough out of the refrigerator at least 20 minutes before you want to work with it.
Preheating. Preheat the oven to 400 degrees F.
Rolling out the dough. Leave the dough in the parchment paper sandwich and roll it out. By rolling it, gently, between the pieces of parchment paper, you will not need to add more flour to the mix. Roll it out to the size of the pie plate, then strip the top piece of parchment paper off the dough. Carefully, flip the dough into the pie plate. Using your fingers, gently press the dough outward, evenly, until you have extended it beyond the edges of the pie plate. You can crimp the edges at this point. If some of the dough falls off the sides, don't worry. Simply reattach the pieces to the crust-to-be by pressing in with your fingers. (Gluten-free pie crust is fragile, but it is also forgiving in the baking.)
Filling the pie crust. Fill the pie crust with the apple filling. Carefully cover the apple filling with another layer of pie crust. Pinch the edges to seal in the apples. Cut a small slit in the top crust to allow the steam from the cooking apples to escape. Put the pie in the oven. Bake for 15 minutes. Lower the oven’s temperature to 350 degrees F and bake the pie for another 30 minutes. Check the pie sporadically to make sure the top is not browning too much. (If it is, cover the pie with some tin foil for the remaining baking time.)
Taking out the pie. The pie is done when you can insert a knife into the apples and have it move through them softly, when the crust is warm and golden, and when the juices from the apples are carmelizing along the edges of the crust. Take the pie out immediately when it has reached this stage. Cool for 20 minutes, then dig in.