PREPARE THE DOUGH: In a large bowl, whisk together the flour, sugar, and salt. Add the cold butter and use a pastry cutter or your fingers to cut it into the flour until the mixture resembles coarse crumbs. Gradually add the ice water, one tablespoon at a time, mixing until the dough just holds together. Form the dough into a disk, wrap it in plastic wrap, and refrigerate for at least 1 hour.
PREHEAT THE OVEN: Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
PREPARE THE FILLING: In a large bowl, toss the sliced apples with granulated sugar, brown sugar, cinnamon, nutmeg, flour, and lemon juice until well coated.
ROLL OUT THE DOUGH: On a lightly floured surface, roll out the dough into a rough 12-inch circle. Transfer it to the prepared baking sheet.
ASSEMBLE THE GALETTE: Arrange the apple slices in the center of the dough, leaving a 2-inch border around the edges. Dot the apples with the small pieces of butter. Fold the edges of the dough over the apples, pleating as necessary.
APPLY EGG WASH: In a small bowl, whisk together the egg yolk and heavy cream. Brush the mixture over the crust's edges and sprinkle the turbinado sugar over the crust and apples.
BAKE THE GALETTE: Bake in the preheated oven for 35-40 minutes, or until the crust is golden brown and the apples are tender.
COOL AND SERVE: Allow the galette to cool on the baking sheet for at least 10 minutes before slicing. Serve warm or at room temperature, perhaps with a scoop of vanilla ice cream.