For The Pie Dough: In the bowl of a food processor fitted with the metal blade, process 1 ½ cups flour, salt, and sugar until combined, about two 1-second pulses. Add butter and shortening and process until dough just starts to collect in uneven clumps, about 10 seconds; dough will resemble cottage cheese curds and there should be no uncoated flour. Scrape bowl with rubber spatula and redistribute dough evenly around processor blade. Add remaining 1 cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 pulses. Transfer mixture into medium bowl.
Sprinkle vodka and water over mixture. Using a folding motion, use a rubber spatula to mix, pressing down on dough until dough is slightly tacky and sticks together. Divide dough into 2 even balls and flatten each into 4-inch disk. Wrap each in plastic wrap and refrigerate at least 45 minutes or up to 2 days.
Heat the oven to 400 degrees F. Line a baking sheet with parchment paper.
To make pumpkin pie filling, scoop the pie filling out of the crust and place in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until smooth, about 30 seconds.
Remove 1 disk of dough from refrigerator and roll out on floured work surface to 12-inch circle, about 1/8 inch thick.
Using a 3-inch round cookie cutter, cut dough into circles. Reroll scraps and cut circles until all dough is used.
Working one 3-inch circle at a time, place 1 tablespoon of pie filling in the center of the circle and fold over. Use a fork to close edges and a small sharp knife to cut two vent holes. Place on prepared baking sheet and repeat until all circles are filled. Repeat the process with the second pie dough disk.
Brush the tops of the pie pockets with egg white and sprinkle with sugar. Bake 13-15 minutes until lightly browned. Remove and let cool slightly before serving.