01 - Combine all-purpose flour, granulated sugar, and salt in a large mixing bowl. Cut in cold, cubed unsalted butter using a pastry cutter or two knives until the mixture forms coarse crumbs.
02 - Gradually incorporate ice water, one tablespoon at a time, mixing just until the dough comes together. Shape into a disk, wrap in plastic, and refrigerate for 30 minutes.
03 - Preheat oven to 400°F. Line a baking sheet with parchment paper.
04 - In a bowl, toss thinly sliced apples with granulated sugar, light brown sugar, ground cinnamon, ground nutmeg, lemon juice, and all-purpose flour. Set aside.
05 - On a lightly floured surface, roll out pastry dough into a 12-inch circle. Transfer pastry to prepared baking sheet.
06 - Arrange apple mixture in the center of dough, leaving a 2-inch border around the edges. Fold the edges over the apples, pleating gently for a rustic appearance.
07 - Brush folded dough edges with beaten egg and, if desired, sprinkle with coarse sugar.
08 - Bake for 35 to 40 minutes, until the crust is deep golden and apples are tender.
09 - Allow galette to cool slightly before serving. Enjoy warm or at room temperature, optionally paired with vanilla ice cream.