Preheat your oven to 375°F (190°C).

In a mixing bowl, combine the flour, butter, sugar, and salt. Mix until resembling coarse crumbs. Add the egg and knead into a smooth dough. Let it rest.

Roll out the dough into a circle about 12 inches in diameter. Place it in a 9-inch pie dish, trim excess dough, and dock the bottom with a fork.

In a separate bowl, toss the sliced apples with sugar, nutmeg, cinnamon, cornstarch, and lemon juice. Let sit to meld flavors.

Pour the apple mixture into the pie crust, spreading it evenly. Dot with pieces of butter.

In a saucepan, heat the milk and vanilla until steaming. Gradually whisk in the remaining sugar until dissolved. Pour over the apple filling.

Bake for 50 minutes or until custard is set and crust is golden brown. Allow to cool for at least 30 minutes before serving.