Preheat the oven to 425°F (220°C).
In a large bowl, combine flour, salt, and sugar. Cut in chilled butter with a pastry blender or fork until the mixture resembles coarse crumbs.
Stir in ice water, one tablespoon at a time, just until dough forms. Divide into two equal balls, wrap in plastic wrap, and refrigerate for at least 1 hour.
In another bowl, combine sliced apples, sugars, spices, cornstarch, vanilla extract, and lemon juice. Toss until evenly coated.
On a lightly floured surface, roll one dough ball to fit a 9-inch pie pan. Transfer to the pan and trim any excess edges.
Pour apple filling into the crust and dot with small butter pieces. Roll the second dough ball and place it over the filling. Trim and crimp edges to seal. Cut small slits on top for steam to escape.
In a small bowl, whisk egg yolk with milk and brush over the top crust.
Bake at 425°F for 15 minutes, then reduce temperature to 350°F (175°C) and bake for another 35–45 minutes, until the crust is golden brown and apples are tender.
Allow the pie to cool on a wire rack before slicing.
