Preheat the oven to 375 degrees F (190 degrees C.)

Combine flour and salt in a large bowl. Cut in butter with 2 knives or a pastry blender until mixture resembles coarse crumbs.

Beat egg yolk in measuring cup; add enough milk to make 2/3 cup total liquid. Stir into flour mixture until mixture is damp.

Divide dough in half. Roll one dough piece on a lightly floured surface; fit into a 9x13-inch pan.

Combine apples, brown sugar, white sugar, cinnamon and nutmeg in a separate large bowl; top dough with apple mixture.

Roll out remaining dough piece; place over apples. Seal edges; cut slits in top to vent.

Beat egg white till frothy; brush on crust.

Bake in the preheated oven until pastry is golden brown, about 50 minutes.