Combine the flour, salt, and sugar in the bowl of a food processor and pulse 3-4 times. Add the butter and pulse until the mixture looks mealy, 5-6 times. Then add the shortening and pulse until incorporated, another 3-5 pulses. Remove the lid and drizzle in the water. Replace the lid and pulse until the mixture begins to come together and pull away from the sides of the bowl.
Dump the mixture onto a clean work surface and squeeze together with your hands to form a smooth ball. Press the ball into a disk shape, wrap in plastic film (we like Stretch-Tite), and refrigerate for at least 1 hour. (You can refrigerate longer, even overnight, just be sure to let the dough sit at room temp for about 15 minutes before attempting to roll.)
Lightly dust a 12-inch x 24-inch piece of wax or parchment paper with flour. Unwrap the dough disk and park on the paper. Lightly flour the top of the dough then roll into an 11-inch circle. Flip over into the pie pan and peel off the paper. Press the dough gently into the pie plate, taking care to get any air out at the corners, then tuck the edges underneath. Crimp with your fingers to form a fluted design at the lip or simply crimp with a fork. Refrigerate crust while making the filling.
Place a rack in the lower third of the oven and set for 350℉.
Place the butter pats in a medium microwave-safe bowl and cover with a paper towel (or you can just re-use the wax paper that the butter was wrapped in). Cook on high-power in three 30 second bursts, or until just melted with a few faint pieces remaining. Set aside to cool for 15 minutes.
Clean your processor's work bowl, add the eggs, the yolk, and the sugar and process for 10 seconds. Remove the lid, add the flour and salt, and pulse for five 1 second pulses. Remove the lid again and add the cooled melted butter, the buttermilk, vanilla bean paste, and nutmeg and blend 10 seconds.
Retrieve the crust from the fridge and place on a half-sheet pan. Pour in the filling and bake for 45 minutes, until the top of the pie puffs slightly and turns golden brown.
Remove to a wire rack to cool for 1 hour. The pie is best served at room temperature with a squeeze of fresh lemon juice.
Note: We prefer the deeper flavor that vanilla bean paste offers in this application, but you can certainly substitute 1 teaspoon of vanilla extract if you prefer.