This is the classic two-crust apple pie perfected during twenty years of baking. The pastry is tender and flaky, and the fruit remains in separate pieces that aren't mushy.
The apples in the pie should hold together when cut and served. To achieve this, the ideal consistency of the surrounding juices should be a thick, silky syrup. Cornstarch or tapioca flour are the best thickeners in an apple pie. Tapioca flour produces a slightly smoother result. It can be ordered by mail. There's always a bit of guesswork in knowing how much thickener to use since the pectin content (and hence the juice-thickening ability) of apples can vary from batch to batch in the market. I prefer using less rather than more I since a slightly runny pie is infinitely preferable to one whose filling is adamant. Let the pie cool completely and leave it at room temperature for several hours before serving. Otherwise, the filling may run.
For the pastry:
For the filling:
To make the pastry in a food processor, with the metal blade in place, process the flour with the salt for 3 seconds. Scatter the butter pieces over the flour; pulse 4 times. Divide the shortening into 4 lumps and add them to the work bowl; pulse 3 times. Scrape the work bowl. Combine the cider vinegar with 6 tablespoons ice water in a 1-cup glass measure. While pulsing very rapidly, add the liquid in a steady stream through the feed tube. Keep pulsing until the dough almost gathers into a ball. There should be several largish clumps of dough in the bowl. Remove the dough from the work bowl and press it gently so that it holds together. Divide in two, with one piece slightly larger than the other. Shape each piece into a 6-inch disk, dust lightly with flour, and wrap tightly in plastic wrap. Refrigerate for 1 hour or longer.
To make the pastry by hand, combine the flour and salt in a mixing bowl. Use a pastry blender to cut the butter into the flour until the pieces are pea-sized. Add the shortening and cut it in until the particles of fat resemble coarse meal. Combine the cider vinegar with 6 tablespoons ice water in a 1-cup glass measure and drizzle the mixture over the dry ingredients while tossing and stirring with a fork. Keep mixing until the dough gathers into a ball. Divide wrap, and chill as described above.
When ready to bake, adjust two oven racks with one in the lowest position and the other in the center position. Place a heavy baking sheet on the lower rack and preheat the oven to 450°F (235°C).
Roll out the larger disk of pastry on a lightly floured surface into a 13-inch circle. Fold the dough into quarters. Center the point of the dough in the center of a 9-inch pie plate, then unfold the dough. Lift the overhanging edge of pastry all around the pie plate so that the pastry lines the pan loosely but snugly; do not stretch the dough. Leave the excess pastry hanging over the edge. Roll out the second piece of dough into a 12 -inch circle. If your kitchen is warm, refrigerate both crusts, placing the top crust on a baking sheet.
To prepare the filling, combine the sugar, cinnamon, nutmeg, tapioca flour (or cornstarch), and salt in a large bowl. Add the apples and toss to combine well. Mix the lemon juice with the Fiori di Sicilia, if using, and drizzle it over the fruit; toss again to combine well.
Turn the filling into the pie shell, mounding the apples in the center. Distribute the butter bits evenly over the filling. Brush the overhanging edge of the pastry lightly with water and cover the filling with the top crust. Press the edges firmly to seal. Using scissors, trim away the excess pastry to within 1/2 inch of the pan's rim. Fold the edge of pastry back on itself to make a standing rim, and flute it. Brush the top crust lightly with water and sprinkle with the sugar. With a small sharp knife, make four slits at right angles to each other between the center and edge of the top crust.
Place the pie on the baking sheet and bake for 15 minutes. Transfer the pie on the baking sheet to the center shelf, reduce the temperature to 350°F (175°C), and continue baking for about 1 hour longer, until the crust is well browned and you can see thickened juices bubbling up through the slits. Cool the pie on a wire rack for at least 6 hours before serving. Refrigerate any leftovers.
Note: A good sharp Cheddar cheese is always welcome with apple pie. Simply place a thin slice or two atop or alongside each serving. Or bake some cheese into the pie by placing a thin layer of Cheddar cheese over the apple filling before putting on the top crust. Cheese and apple pie are best when the pie is eaten warm; if the filling oozes, that's all right.