To make the pastry: Combine both flours, sugar and salt in the bowl of a food processor fitted with the metal blade. (See NOTES below for instructions on making pastry by hand). Pulse a few times to combine the dry ingredients. Add the butter pieces and pulse until the mixture resembles pebbles and coarse sand without any pieces of butter larger than a lima bean. Whisk the egg yolk and the ice water, remove the lid of the food processor and drizzle the liquid evenly over the flour-butter mixture. Replace the lid and pulse just until the dough begins to hold together. Do not over mix. You will still see bits of butter in the dough. Turn dough out onto plastic wrap or wax paper and gather the dough into a disk about an inch thick; wrap and refrigerate at least 30 minutes or up to one day. (You can also freeze pastry dough, tightly wrapped, for up to 3 months. Thaw in refrigerator before using).
Preheat oven to 400ºF.
Place dough in center of a 15-inch square piece of lightly floured parchment paper. If the dough is too cold to roll easily, let it stand for about 5 minutes to soften slightly. Roll dough with a rolling pin into a 12-inch circle, starting from the center of dough and rolling toward the outside edges. If the dough begins to stick to the rolling pin, sprinkle the dough with a little flour. If it is too dry, add a very small sprinkle of water, preferably with a spray bottle, to moisten dough. Slide dough circle along with the parchment paper onto a large rimmed baking sheet and refrigerate while making the filling.
Combine brown sugar, cornstarch and cinnamon in a medium bowl. Add apple slices and toss with a rubber spatula until evenly coated. Remove dough circle from refrigerator and spoon fruit filling evenly onto dough, leaving about an inch and a half of dough uncovered around the edges. Sprinkle small butter cubes over filling. Turn over dough edges onto filling and gently press folded areas. Lightly whisk egg white and brush pastry edges; sprinkle pastry and filling with raw sugar if desired.
Bake in the center of the preheated oven until pastry is golden brown and filling is bubbly, about 45 to 50 minutes. Some juices may spill out onto the parchment which just adds to the rustic beauty of a galette. Let cool slightly or to room temperature. Galette is best served the day it is baked.
Makes about 8 servings.