Prepare the pie crust by mixing flour, sugar, and salt together.
Cut in the cold butter until the mixture resembles coarse crumbs.
Gradually add cold water, a tablespoon at a time, until the dough holds together.
Divide the dough in half and refrigerate for at least 1 hour.
Preheat your oven to 375°F (190°C).
Roll out one portion of the dough to fit a rimmed baking sheet.
Transfer the rolled-out dough to the baking sheet and trim the edges.
In a bowl, combine the sliced apples, brown sugar, cinnamon, lemon juice, and cornstarch.
Pour the apple mixture onto the crust and spread it evenly.
Roll out the second portion of dough and place it over the apples, sealing the edges.
Brush the top with beaten egg for a golden finish.
Bake for 45-50 minutes, or until the crust is golden and the filling is bubbling.
Let the pie cool for at least 30 minutes before slicing.