In a bowl, combine flour and salt. Cut in cold butter until mixture resembles coarse crumbs.
Add ice water 1 tablespoon at a time until dough comes together. Shape into a disc, wrap, and refrigerate for 30 minutes.
Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a large bowl, toss sliced apples with granulated sugar, cinnamon, and lemon juice.
On a floured surface, roll out the dough into a 12-inch circle. Transfer to baking sheet.
Arrange apple slices in the center, leaving a 2-inch border. Fold edges over filling, pleating as needed.
Brush crust with beaten egg and sprinkle with coarse sugar if desired.
Bake for 40–45 minutes or until crust is golden and apples are tender.
Let cool slightly before slicing and serving.