01 - Combine buckwheat flour, all-purpose flour, granulated sugar, and sea salt in a large mixing bowl. Incorporate cold, cubed unsalted butter using a pastry blender or fork until the mixture resembles coarse crumbs. Gradually add ice water, stirring just until the dough binds together. Form the dough into a disc, wrap tightly in plastic, and refrigerate for at least 30 minutes.
02 - In a separate bowl, toss thinly sliced apples with brown sugar, lemon juice, ground cinnamon, ground nutmeg, cornstarch, and vanilla extract until evenly coated. Set aside.
03 - Preheat oven to 400°F. Line a baking sheet with parchment paper. On a lightly floured work surface, roll out the chilled dough into a 12-inch circle. Transfer dough to the prepared baking sheet. Mound apple filling in the center, leaving a 2-inch border around the edges.
04 - Carefully fold the dough edges over the apples, pleating as needed to create rustic folds. Brush the exposed pastry with beaten egg. Sprinkle turbinado or coarse sugar over the crust if desired.
05 - Bake for 40 minutes, or until the crust is golden brown and apples are tender. Remove from oven and allow to cool slightly before slicing and serving.