In a large bowl, whisk together the flour, sugar, and salt. Cut in the cold, cubed butter until the mixture resembles coarse crumbs. Beat in the egg, then add the ice water a tablespoon at a time, mixing just until the dough comes together. Divide into two disks, wrap, and refrigerate.

In a skillet over medium heat, melt the butter and cook the diced apples until just softened. Stir in the brown sugar, cinnamon, nutmeg, lemon juice, cornstarch, salt, and vanilla. Cook until thickened, then remove from heat and let cool completely.

Preheat the oven to 375°F and line a baking sheet with parchment. Roll the dough to 1/8-inch thickness and cut into 5 to 6-inch rounds. Spoon 2 tablespoons of cooled filling onto each round, fold into a half-moon, and crimp the edges with a fork to seal. Whisk the second egg with the water and brush over each empanada. Sprinkle with turbinado sugar and bake until golden brown, 25 to 30 minutes.