To make the pie dough, combine the flour, sugar and salt in a food processor. Pulse to combine. Add the cold butter and shortening on top and pulse until mixture resembles coarse crumbs. (It should roughly hold together if you grab a handful and squeeze.)
Pour mixture into a bowl and sprinkle with vodka or water. Using a rubber spatula, stir together then press the dough into itself until it sticks together. If it will not come together, add additional water one tablespoon at a time.
Divide dough into two pieces, one slightly larger than the other, and flatten into disks. Wrap in plastic wrap and refrigerate for at least an hour (can be left in the fridge for up to two days or frozen for up to two months).
Let soften for about 10 minutes (or until malleable if frozen). Roll larger piece and set into pie plate, reserving smaller piece for the top.
To make filling, core, peel and slice apples into 1/4 inch slices. Toss slices with lemon juice in a large bowl. Add flour, sugar, brown sugar, salt and cinnamon, mixing until the apples are well coated. Transfer to a large pan or stock pot and cook, covered, over medium heat for about 15 minutes, stirring every few minutes or until apples have softened but aren’t mushy. Set aside to cool.
Preheat oven to 400 degrees.
Once apples are about room temperature, transfer to the lined pie plate. Roll the remaining pie crust and form a lattice top (see note) on top of your pie. If desired, brush with a beaten egg mixed with a tablespoon of milk, and sprinkle with sugar.
Set pie plate on baking sheet and bake at 400 degrees for 20 minutes. Reduce oven to 350 degrees and continue baking for an additional 40- 45 minutes. Keep an eye on the crust and if it begins to get too brown, lightly tent the pie with foil.
Cool on rack before serving.