In a large bowl, whisk flour, sugar, and salt. Cut in cold butter until mixture resembles coarse crumbs.

Drizzle ice water a tablespoon at a time, gently tossing until dough clumps without feeling wet.

Divide dough into two disks, wrap in plastic, and refrigerate for 1 hour.

Preheat oven to 375°F (190°C) and position a rack in the lower third.

In a bowl, toss sliced apples with brown sugar, cinnamon, cornstarch, lemon juice, and salt.

On a floured surface, roll one dough disk to ¼-inch thickness, fit into a pie pan, and trim edges.

Pour apple mixture into crust, mounding slightly at center, then dot with butter pieces.

Roll second disk to ¼-inch, place over filling, crimp edges to seal, and trim overhang.

Whisk egg with water and brush over crust, then sprinkle with coarse sugar.

Bake for 50–60 minutes until crust is golden brown and filling bubbles through vents.

Let pie rest on a wire rack for at least 2 hours before serving.