With the rack in the lowest position, preheat the oven to 190 °C (375 °F).
In a small bowl, combine the egg yolk and milk. Set aside.
In a large bowl, combine the brown sugar, cornstarch, cinnamon, and nutmeg. Stir in the apples and butter.
Line a 23-cm (9-inch) pie plate with a pie crust. Fill with the apple mixture and lightly press. Brush the edges of the dough with water. Top with the second crust. Make an incision in the center. Remove any excess dough. Pinch the top and bottom crust together with a fork or your fingers to seal. Brush with the egg wash. Bake for about 55 minutes or until the crust is golden brown. Cool on a wire rack.