To make the dough, add All-Purpose Flour (3/4 cup), Granulated Sugar (1 tablespoon), and Salt (1/2 teaspoon) to a food processor and process until combined, about 5 seconds.
Sprinkle Unsalted Butter (6 tablespoon) and Vegetable Shortening (4 tablespoon) on top and continue processing until mixture begins to form uneven clumps with no remaining floury bits (about 10 seconds).
Scrape down sides of bowl and redistribute dough around blade. Sprinkle remaining All-Purpose Flour (1/2 cup) over dough and pulse until mixture is evenly distributed into pieces around bowl (4 to 6 pulses).
Transfer mixture to a medium bowl. Sprinkle Vodka (2 tablespoon) and Cold Water (2 tablespoon) over mixture. Using a stiff silicone spatula, stir and press down until it sticks together.
Turn pie dough onto sheet of plastic wrap and shape into round 4-inch shape. Wrap tightly in plastic and refrigerate for at least 1 hour or up to 2 days.
Preheat oven to 350 degrees F (175 degrees C).
Toast the Pecans (2 cup) on a baking sheet for about 8 minutes, tossing them halfway through. After they have cooled, chop into desired pieces. I usually toast a few additional pecans to use as garnish for the top of my pie.
Remove dough from refrigerator and allow to soften slightly (about 10 minutes) before rolling. Roll dough into a 12-inch circle on floured counter.
Lightly sprinkle flour into bottom of glass or ceramic pie plate (this will keep your crust from sticking to the bottom of the pie plate.)
Roll dough loosely around your rolling pin and unroll into the pie pan, leaving at least a 1-inch overhang on each side. Working in a circular motion, ease dough into place by gently lifting the edge of dough with one hand while pressing into plate bottom with the other hand. Wrap with plastic wrap and refrigerate until dough is firm, about 30 minutes.
Trim overhang to ½ inch beyond lip of pie plate. Fold overhang under itself; folded edge should be flush with edge of pie plate. Using your thumb and forefinger, flute and crimp edge of dough evenly around pie plate. Use a fork to prick the dough all over the bottom and sides of the pie plate. Wrap in plastic wrap and refrigerate again until dough is firm, about 15 minutes.
Adjust the oven rack to the lowest position and preheat to 425 degrees F (220 degrees C).
Remove pie plate from refrigerator, brush the crust edge with an Egg (1) wash.
Line crust with aluminum foil or parchment paper, covering edges to prevent browning, and fill with pie weights - filling the whole way up to the rim of the pie plate. Bake for 10 minutes (the crust will look dry and pale in color).
Remove foil/parchment and weights, rotate plate, and bake 4 to 7 additional minutes until crust is light golden brown.
Remove pie plate from oven. The crust must still be warm when you add the filling. As soon as the pie shell comes out of the oven, decrease the oven temperature to 275 degrees F (135 degrees C) and adjust oven rack to middle position.
While crust is baking, melt the Unsalted Butter (6 tablespoon) in the top of a double boiler, with barely one inch of water in the lower pan, maintained at just below a simmer – make sure that water does not touch the bottom of the bowl.
Remove from heat and stir in the Dark Brown Sugar (1 cup) and Salt (1/2 teaspoon) with a wooden spoon until the butter is absorbed.
Slowly whisk Egg (3) into the sugar mixture, then whisk in Light Corn Syrup (3/4 cup) and Vanilla Extract (1 tablespoon), stirring constantly until smooth.
Return the bowl to hot simmering water; continue heating and stir until the mixture is shiny and hot to the touch, about 130 degrees F (55 degrees C) on an instant-read thermometer. Remove from the heat; stir in the toasted pecans.
Pour the pecan mixture over the back of a spoon into the warm pie shell (this will prevent your crust from cracking).
Bake on the middle rack until the pie looks set and yet soft, like gelatin, when pressed gently with the back of a spoon, 50 to 60 minutes. Rotate pie plate halfway through baking.
Transfer the pie to a rack; cool completely until filling has set (2 to 4 hours). It is easiest to slice the pie when it is chilled, but best served at room temperature or warmed slightly.