Prepare the Pie Dough: Dice the unsalted butter and shortening and place it in the freezer while preparing the flour mixture. In a food processor fitted with a steel blade, pulse flour, salt, and sugar to combine; add the chilled butter and shortening pieces and pulse until the mixture resembles a coarse crumble with only a few larger pieces, about 8 to 12 pulses. In a small bowl, combine 5 tablespoons of ice water, 1 tablespoon of pure vanilla extract, and 1 tablespoon of apple vinegar.
With the machine running, pour the ice water mixture down the feed tube and pulse the machine until the mixture is evenly moistened and crumbly; don't let the dough form into a ball in the machine. Turn the pie dough onto a work surface, and bring the dough together by hand. Use a bench scraper to divide the dough into two equal pieces. Shape into flat disks and wrap in plastic wrap. Refrigerate for at least 30 minutes, preferably overnight. The dough can be refrigerated for up to 3 days or frozen for up to 6 weeks, tightly wrapped. (Thaw frozen dough in the refrigerator before rolling it out.)
Lightly dust a work surface and a rolling pin with flour. Place one chilled pie disk on the work surface and let the dough sit on the countertop for 5 to 10 minutes so it's malleable enough to roll. Reserve the other half, wrapped tightly, and refrigerated. Lightly dust the dough with additional flour. Roll half of the dough ⅛ inch / 3 mm thick using even strokes. Turn it occasionally to produce an even shape and to keep it from sticking to the work surface. Work from the center toward the edges, rolling in different directions. If the dough softens too fast, chill in the refrigerator until firm, 2–5 minutes.
Carefully transfer the rolled dough into the pie dish. Position the dough so that it completely covers the entire dish. Settle the dough into the dish, pressing the dough gently against the dish. Use a ball of scrap dough to gently press the pie dough into the pie dish and dock the bottom of the crust if necessary. Trim the excess dough from the rim, leaving enough to seal a top crust in place.
In a large bowl, toss the apples with the sugar, cinnamon, nutmeg, vanilla, salt, lemon juice, butter, cornstarch, and tapioca. Fill the pie shell with apple mixture. Roll out the top crust in the same manner as the bottom crust (⅛ inch / 3 mm thick) and carefully lay the top crust over the filling. Press the dough around the rim to seal the top and bottom crusts. Trim away excess overhang, seal and crimp the edges (lightly flour your fingers if the dough is sticking), and cut several vents atop the pie to allow steam to escape. Refrigerate for 1 hour.
Bake: Brush the crust lightly with egg wash, heavy cream, or milk, and sprinkle with coarse sugar. Place a rack in the lower third of the oven and preheat the oven to 375 degrees F. Bake the pie on a baking sheet until the crust is golden, about 45 minutes to 1 hour, or until the internal temperature registers approximately 175 ºF. Cover the edges with a crust shield or foil if the pie crust edges are browning too quickly. The dough should appear dry.
If the dough has been rolled out unevenly, the thicker portion may appear moist, indicating that the dough is not fully baked. The Apple Pie Filling should be bubbling. Cool the pie on a wire rack for at least 2 to 3 hours before slicing it to serve. The Apple Pie keeps well at room temperature (covered) for 24 hours or refrigerated for up to 4 days. Serve warm or at room temperature with spiced whipped and vanilla ice cream or a hot cup of coffee.🥧☕
Camila's Tips: If you don't have tapioca starch, you can simply use 2 tablespoons of cornstarch and 2 tablespoons of all-purpose flour.