1¼ cups all-purpose flour plus extra for dough and surface
2 tablespoons powdered sugar
½ teaspoon sea salt
8 tablespoons chilled unsalted butter; cut into ¼-inch pats
2 tablespoons vegetable shortening; frozen solid and cut
1 large chilled egg white; mixed with ice water
1 large egg yolk; beaten
⅛ teaspoon water
1. Preheat oven to 400ºF.
2. Mix flour, sugar, and salt in food processor fitted with steel blade. Scatter butter and shortening over dry ingredients and pulse until mixture resembles coarse cornmeal, 10 to 15 seconds. Turn mixture into medium bowl.
3. Sprinkle egg white mixture over flour mixture and, with blade of rubber spatula, use folding motion to mix. Press down on dough with broad side of spatula until dough sticks together. Shape dough into ball with hands, and then flatten into 4-inch disk. Dust dough lightly with flour, wrap tightly in plastic wrap, and place in refrigerator for at least 1 hour or up to 2 days.
4. Roll dough on lightly floured surface into 13-inch circle and transfer to 9-inch pie pan, preferably glass. Press dough into corners and sides of pan, being careful not to stretch dough. Trim edges of dough to make ½-inch overhang. Tuck overhanging dough under so that folded edge is flush with rim of pan. Flute edge.
5. Chill shell until firm, about 1 hour. Prick sides and bottom with fork and line entire shell with heavy-duty aluminum foil, pressing foil firmly against shell and extending it over fluted rim. Prick foil with fork and return shell to refrigerator while oven is heating.
6. Adjust oven rack to center position and heat oven to 400ºF
7. Bake, pressing once or twice with mitt-protected hands, if necessary, to flatten any puffing, until crust is firmly set, about 15 minutes. Remove foil and continue to bake until bottom begins to color, about 10 minutes longer. Remove from oven, brush sides and bottom with egg yolk, and return to oven.