Whisk flour, sugar, and salt in a bowl.
Cut in butter until the mixture resembles coarse crumbs.
Add water, stirring until dough is moistened. Add more water if needed.
Turn dough onto a floured surface, shape into a ball, and flatten into a disc.
Wrap dough in plastic and refrigerate for at least 1 hour (up to 3 days).
For the filling, mix apples, brown sugar, flour, lemon juice, cinnamon, and nutmeg in a bowl. Refrigerate.
Roll dough into a 12-inch circle and transfer to a baking sheet lined with parchment paper.
Arrange apple filling on the dough, leaving a border, and fold edges over.
Brush edges with egg wash, sprinkle with sugar, and refrigerate for 15–20 minutes.
Preheat oven to 400°F. Bake for 35–36 minutes until golden. Let cool for 10 minutes before serving.