Make the Apple Filling
- Place the peeled, sliced apples in a large bowl.
- Add the vanilla, ¼ cup flour, lemon zest and juice, granulated sugar and brown sugar to the bowl with the apples. Sprinkle the cinnamon, nutmeg and salt over the apples. Stir to combine. Set aside while you make the pie crust.
Make the Pie Crust
- Place the flour, sugar and salt in the bowl of a food processor fitted with the steel blade. (Alternatively, the pie crust dough can be made by hand in a large bowl using a pastry cutter or your fingers to cut in the butter.)
- Pulse to combine the dry ingredients. Add the cold butter cubes and pulse about 10 times, until the largest butter pieces are the size of small peas.
- Add the ice-cold water and pulse just until the dough comes together.
- Transfer the dough to a lightly floured work surface and form it into a ball. Cut the ball in half and shape each half into a round disk. Wrap one of the disks in plastic wrap and place it in the refrigerator.
- On a lightly floured work surface, roll the second disk out to a 12-inch round and transfer it to a deep-dish pie dish. (This is easily done by wrapping the dough round around your rolling pin to help move it.)
Assemble the Pie
- By this time, the apples should have released some of their juices. Stir the apple mixture to make sure everything is well combined and then pour the apples and their juices into the pie crust.
- Roll out the second pie dough disk to a 12-inch round. You can place the dough round on top of the pie as is, or you can make a lattice-top pie crust. If putting the full dough round on top of the pie, cut a few slits in the top crust to allow steam to escape as the pie bakes.
- To make a lattice top pie crust: Cut the second dough round into ½-inch strips. Place the longest strip down the center of the pie. Reserving every other dough strip to go in the other direction on the pie, lay strips across the pie with just a little bit of space between. Then weave in strips going the opposite direction on the pie.
- Brush the pie crust with milk (to help with browning and to help the coarse sugar stick) and sprinkle with coarse sugar, if desired.
- Refrigerate pie for 30 minutes before baking.
- Meanwhile, preheat oven to 400° F with a rack in the lower third of the oven.
- Bake the pie at 400° for 20 minutes, then reduce oven temperature to 350° F. Continue baking the pie for 40-50 minutes more, until the filling is bubbly. Check on the pie partway through the baking time and tent it with foil as needed to prevent the crust from over-browning.
- Let the pie cool at room temperature for at least 2 hours before serving to allow the filling to thicken.
- Store pie at room temperature for up to one day, or in the refrigerator, covered with plastic wrap, for up to 5 days. Pie can also be frozen, wrapped tightly, for up to 3 months.