1. To make the dough: Process the flour, salt and sugar in a food processor until combined. Add the shortening and butter and process until the mixture resembles coarse crumbs, about 10 seconds. With the machine running, pour ice water through the feed tube in a steady stream until the dough just holds together without being too wet or sticky; do not process more than 30 seconds. test the dough by squeezing a small amount together: If it is crumbly, add a bit more water. turn out the dough onto a work surface. divide in half. Place each half on a sheet of plastic wrap; flatten into disks. Wrap in plastic, and refrigerate at least 1 hour or up to 2 days. Dough can be frozen, wrapped in plastic, up to 3 weeks; thaw in refrigerator.
2. Adjust an oven rack to the lowest position, place a rimmed baking sheet on it, and heat the oven to 500 degrees F. Remove one piece of dough from the refrigerator (if refrigerated longer than 1 hour, let stand at room temperature until malleable.
3. Roll the dough on a lightly floured work surface to a 12-inch circle. Transfer the dough to a 9-inch pie plate, leaving the dough that overhangs the lip of the pie plate in place; refrigerate the dough-lined pie plate.
4. Bring 3 quarts of water to a boil in a large saucepan and fill a large bowl with 2 quarts cold water and 2 trays ice cubes. With a paring knife, score a small x at the base of each peach. Lower the peaches into the pan of boiling water with a slotted spoon. Turn the peaches occasionally and simmer until their skins loosen, 30 seconds to 1 minute, depending on the ripeness of the peaches. Transfer the peaches to a bowl of ice water. Let stand to stop the cooking process, about 1 minute and cool. Starting from the scored x, peel each peach. Use a paring knife to lift the skin from the flesh and pull the skin off in strips. Halve, pit, and cut each peeled peach into 3/8-inch slices.
5. Toss the peach slices, lemon juice, 1 cup granulated sugar, cinnamon, nutmeg, salt and instant tapioca in a medium bowl.
6. Roll out the second piece of dough to a 12-inch circle. Turn the peach mixture into the dough-lined pie plate. Place the second piece of dough over the filling. Trim the top and bottom edges to ½ inch beyond the pan lip. Tick this rim of dough underneath itself so that the folded edge is flush with the pan lip. Flute the edge or press with fork tines to seal. Cut 4 slits in the dough top. In a small bowl, whisk together the egg yolk and heavy cream to make the egg wash. Brush the entire surface of the pie with egg wash, and sprinkle with the remaining 1 tablespoon granulated sugar.
7. Lower the oven temperature to 425 degrees. Place the pie on the baking sheet and bake until the crust is set and begins to brown, 25 to 30 minutes. Rotate the pie and reduce the oven temperature to 375 degrees; continue baking until the crust is deep golden brown and juices bubble, 25 to 30 minutes longer. Cool the pie on a wire rack for at least 2 hours before serving.