Sift dry ingredients together in a large bowl. Cut the butter into small chunks (about 1/2" thick) and add to dry ingredients. Work it into the dry ingredients using a pastry cutter or your finger tips, mashing until the butter has crumbled into pea-size pieces.
Make a well in the dry ingredients. Pour the egg and apple cider vinegar into the well, and use a fork to stir gently, outwards from the center. Once all the ingredients are incorporated, drizzle the ice-cold water into the mixture very slowly, just a little at a time. Only add water until the mixture has become a cohesive ball of dough that's just moist enough to handle without being wet.
Place ball between two large pieces of parchment paper. Using hands or rolling pin, gently push the dough outward, equally in all directions, until it is a pie-sized thick, even disc of dough. Leave between parchment paper layers and seal well in plastic wrap or ziploc bag. Refrigerate for at least two hours. Remove the dough from the refrigerator and allow to sit at room temperature for 15-20 minutes.
Leaving the dough in between two parchment paper layers, roll it out gently, as thin as you can. When the dough is between 1/4" and 1/3" thick, remove the top layer of parchment and even out the edges of the crust. Place a pie pan with the top side down over the dough (centered) and then carefully flip paper, dough and pan over so that the dough drapes into the pan. Carefully peel away parchment. Use your fingers to make sure the dough touches all the corners of the pan. If any holes have already formed at this point, mend them with a finger or pastry brush dampened in egg white or water, or with excess dough.
Use in your favorite pie recipes, or roll out for use in a galette or other pastry. You can prebake this crust if you like, but it doesn't require prebaking.