I like cinnamon in my apple pie, but no nutmeg or other spices. However, vanilla adds something special and a little different to this otherwise classic two-crusted apple pie. Also, I find that a blend of apples is best, taking advantage of what each one has to offer. Try a mix of Northern Spy and Golden Delicious. Or Granny Smith and Cortland. Or Baldwin, Northern Spy and Golden Delicious. It's not such a bad thing to have to make this pie several times to find your favorite mix. Use the lesser amount of sugar with a sweeter blend of apples, more sugar with the higher proportion of Granny Smith, for example. If you can find Baldwin apples, try them. They have a wonderfully complex, winey flavor.
Also, peeling apples by hand is certainly doable, but there are apple peelers on the market that make quick work of the job. Some have a vice like clamp that attaches to the table, others have a broad, suction cup base which I find to work better. Both have a rotating spit that holds the apple, which when turned via a crank, pushes the apple against a sharp peeler. The apple is cored, peeled and cut into 1/4-inch slices in one action. This tool is not cheap (about $40), but when apples appear fresh in the Fall, it can make the difference between being motivated to get in the kitchen with a few bushels, or only dreaming about how great it would be to have your freezer stocked with applesauce.
Have you ever sliced into an apple pie and found a large amount of headroom between the cooked down apple filling and the top crust? That's because the apples were left in large chunks creating a lot of air space between them when raw. Thin slices eliminate this problem. You get more apple bang for your buck this way and that's why we eat apple pie in the first place.
Spray a 9 1/2-inch deep dish pie plate with pan coating. Roll out bottom crust and fit into pie plate (see Working with Pie and Tart Dough, page xx).. Refrigerate while assembling remaining ingredients.
Peel and core apples. Slice into 1/4-inch slices by hand or machine. Place in mixing bowl with sugar, tapioca, lemon juice, vanilla extract and cinnamon (Start with the lesser amount of vanilla to see if you like it. Try the full teaspoon next time). Toss to mix.
Pile into pie crust. Dot with butter. Refrigerate while rolling out top crust.
Roll out top crust and place on top of apples. Seal and crimp edges. Make a steam vent. Brush pie with milk. Combine sugar and cinnamon and sprinkle over pie. Freeze for 15 minutes while you preheat oven to 400 degrees F.
Place pie on parchment lined half-sheet pan. Place in oven, turn oven down to 375 degrees F and bake for 45 minutes. Check to see how pie is browning. Continue to bake for approximately 15 more minutes or until crust is golden brown and filling is bubbling.
Cool at room temperature for 30 minutes before serving to allow juices to thicken.
Serve with Vanilla Ice Cream or Triple Vanilla Ice Milk for an a la mode treat.