Adjust rack in oven to lower third. Preheat oven to 425 degrees F (220 degrees C).

Combine 3 cups flour, 1 1/2 cup plus 1 tablespoon cold butter, 2 tablespoons sugar, and salt in a food processor. Pulse until coarse meal forms. Add remaining 1 cup flour; pulse to incorporate. Alternate adding vodka and water to flour mixture a tablespoon at a time, pulsing until dough forms into a ball.

Divide the dough in half and shape into balls. Roll out each ball to fit a 12-inch deep-dish pie plate. Place bottom crust in pie plate. Brush 1/2 of egg wash over bottom pie crust.

Bring 3 quarts water to a boil in a large stock pot. Remove from heat. Add apples and let stand 10 minutes; drain. Toss lemon juice and zest together with apples in a large bowl.

Combine 1 cup sugar, 2 tablespoons flour, apple pie spice, and cinnamon together in a small bowl.

Place 1 layer of apples onto pie crust; sprinkle with some of the spice mixture. Repeat with remaining apples and spice mixture, reserving 1 tablespoon of the spice mixture for top crust. Cover apples with top pie crust; brush with remaining egg wash and sprinkle with remaining spice mixture.

Bake in the preheated oven for 20 minutes. Reduce temperature to 350 degrees F (175 degrees C); bake until golden brown, 25 to 30 minutes more.