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Pulse flour, salt, and sugar in a food processor workbowl fitted with the steel blade. Add butter and pulse to mix in five 1-second bursts. Add shortening and continue pulsing until flour is pale yellow and resembles coarse cornmeal, four or five more 1-second pulses. Turn mixture into medium bowl. (To do this by hand, freeze the butter and shortening, grate it into the flour using the large holes of a box grater, and rub the flour-coated pieces between your fingers for a minute until the flour turns pale yellow and coarse.)
Sprinkle 6 tablespoons ice water over mixture. With blade of rubber spatula, use folding motion to mix. Press down on dough with broad side of spatula until dough sticks together, adding up to 2 tablespoons more ice water if dough will not hold together. Squeeze dough gently until cohesive and divide into two equal balls. Flatten each into a 4-inch-wide disk. Dust lightly with flour, wrap separately in plastic, and refrigerate at least 30 minutes, or up to 2 days, before rolling.
Remove dough from refrigerator. If stiff and very cold, let stand until dough is cool but malleable. Adjust oven rack to center position and heat oven to 425 degrees.
Roll one dough disk on a lightly floured surface into a 12-inch circle. Fold dough in quarters, then place dough point in center of 9-inch Pyrex regular or deep dish pie pan. Unfold dough.
Gently press dough into sides of pan leaving portion that overhangs lip of pie plate in place. Refrigerate while preparing fruit.
Peel, core, and cut apples into 1/2-to-3/4-inch slices and toss with 3/4 cup sugar and lemon juice and zest through allspice. Turn fruit mixture, including juices, into chilled pie shell and mound slightly in center. Roll out other dough round and place over filling. Trim top and bottom edges to 1/2 inch beyond pan lip. Tuck this rim of dough underneath itself so that folded edge is flush with pan lip. Flute edging or press with fork tines to seal. Cut four slits at right angles on dough top. Brush egg white onto top of crust and sprinkle evenly with remaining 1 tablespoon sugar, (omit if freezing unbaked pie, see below).
Bake until top crust is golden, about 25 minutes. Reduce oven temperature to 375 degrees; continue baking until juices bubble and crust is deep golden brown, 30 to 35 minutes longer. Transfer pie to wire rack; cool to almost room temperature, at least 4 hours.
Do-Ahead: Freeze the unbaked pie for two to three hours, then cover it with a double layer of plastic wrap, and return it to the freezer for no more than two weeks. To bake, remove the pie from the freezer, brush it with the egg wash, sprinkle with sugar, and place directly into a preheated 425 degree oven. After baking it for the usual fifty-five minutes, reduce the oven to 325 degrees, cover the pie with foil so as not to overcook the crust, and bake for an additional twenty to twenty-five minutes.
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