Pulse flour, salt and sugar in a food processor fitted with steel blade until combined. Add shortening and process until mixture has texture of coarse sand, about 10 seconds. Scatter butter pieces over flour mixture; cut butter into flour until mixture is pale yellow and resembles coarse crumbs, with butter bits no larger than small peas, about ten 1-second pulses. Turn mixture into medium bowl.

Sprinkle 8 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 it will not come together. Divide dough into two pieces, one slightly larger than the other. Flatten larger piece into a rough 5-inch square and smaller piece into a 4-inch disk; wrap separately in plastic and refrigerate at least 1 hour or up to 2 days before rolling.

Adjust oven rack to lowest position and heat rimmed baking sheet and oven to 500°F.

Remove one piece of dough from refrigerator (if refrigerated longer than 1 hour, let stand at room temperature until malleable). Roll dough on lightly floured work surface or between two large sheets of plastic wrap to 12-inch disk. Transfer dough to pie plate by rolling dough around rolling pin and unrolling over 9 1/2-inch pie plate or by folding dough in quarters, then placing dough point in center of pie plate and unfolding. Working around circumference of pie plate, ease dough into pan corners by gently lifting dough edges with one hand while pressing around pan bottom with other hand. Leave dough that overhangs lip of plate in place; refrigerate dough-lined pie plate.

Peel, core and cut apples in half, and in half again width-wise; cut quarters into 1/4-inch slices and toss with lemon juice and zest.

In a medium bowl, mix 3/4 cup sugar, flour, salt and spices. Toss dry ingredients with apples. Turn fruit mixture, including juices, into chilled pie shell and mound slightly in center.

Roll out second piece of dough to 12-inch disk 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 on dough top. If pie dough is very soft, place in freezer for 10 minutes. Brush egg white onto top of crust and sprinkle evenly with remaining 1 tablespoon sugar.

Place pie on baking sheet and lower oven temperature to 425°F. Bake until top crust is golden, about 25 minutes. Rotate pie and reduce oven temperature to 375°F; continue baking until juices bubble and crust is deep golden brown, 30-35 minutes longer.

Transfer pie to wire rack; cool to room temperature, at least 4 hours.