Melt butter and set aside to cool to room temperature,
Prepare a pie plate with your bottom pie crust, and preheat the oven to 425°F.
Mix together the sugar, flour, and cinnamon, and set aside.
Whisk the whole egg with 2 yolks and milk, and add the sugar mixture. Whisk together until smooth to make a custard.
Working quickly so they don’t turn brown, peel, core, and grate the 4 granny smith apples into a mixing bowl. Drizzle the cooled melted butter on top, and mix until all apples are coated. Pour in the custard mixture, and stir to combine.
Pour apple filling into crust, and top with strips of dough to form a lattice. Flute the edges, and decorate with a cut out of an apple and leaves, if desired. Do NOT completely cover the pie with a crust because the custard need to breath in order to bake properly.
In a small bowl, whisk the remaining egg with a fork. Brush the edges of the pie crust with the egg wash.
Cover edges with foil.
Bake at 425°F for 15 minutes, then reduce the oven temperature and bake at 350° for 35-45 minutes until golden brown. Watch closely. You may want to remove foil from edges for last 15 minutes, if the crust is still too wet and raw looking.
Remove from the oven, and cool to let the custard set.
Serve with plain or garnished with whipped cream or ice cream.