Combine 2.5 cups flour and a pinch of salt in a large chilled mixing bowl.
Cut the frozen butter into the flour using a pastry cutter until the mixture resembles coarse crumbs.
Add ice water one tablespoon at a time until the dough holds together when squeezed.
Divide the dough into two disks, wrap tightly, and refrigerate for one hour.
Peel, core, and slice apples into thin, uniform pieces.
Toss the apples with sugar, cinnamon, and one tablespoon of flour in a separate bowl.
Roll out one dough disk on a floured surface and fit it into a nine-inch pie plate.
Pour the apple mixture into the crust, top with the second rolled-out dough disk, crimp the edges to seal, and cut vents in the top.
Bake at 375°F for 50 minutes or until the crust is golden brown and the filling is bubbling.