1. Process the flour, salt, and sugar in a food processor until combined. Add the shortening and process until the mixture has the texture of course sand, about 10 seconds. Scatter the butter pieces over the flour mixture; cut the butter into the flour until the mixture is pale yellow and resembles coarse crumbs, with butter bits no larger than small peas, about ten 1-second pulses. Turn the mixture into a medium bowl.
2. Sprinkle 4 tablespoons of the ice water over the mixture. With a rubber spatula, use a folding motion to mix. Press down on the dough with the broad side of the spatula until the dough sticks together, adding up to 1 tablespoon more ice water if the dough will not come together. Flatten the dough into a 4-inch disk. Wrap in plastic and refrigerate at least 1 hour, or up to 2 days, before rolling.
3. Remove the dough from the refrigerator (if refrigerated longer than 1 hour, let stand at room temperature until malleable). Following the illustrations on page 146, roll the dough on a lightly floured work surface or between 2 sheets of parchment paper or plastic wrap into a 12-inch circle. Transfer the dough to a 9-inch pie plate by rolling the dough around the rolling pin and unrolling over the the pan. Working around the circumference of the pie plate, ease the dough into the pan corners by gently lifting the edge of the dough with on hand while gently pressing into the pan bottom with the other hand. Trim the dough edges to extend about ½ inch beyond the rim of the pan. Fold the overhang under itself; flute the dough or press the tines of a fork against the dough to flatten it against the rim of the pie plate. Refrigerate the dough-lined pie plate until firm about 40 minutes, then freeze until very cold, about 20 minutes.
4. Adjust an oven rack to the lower-middle position and heat the oven to 375 degrees. Remove the dough-lined pie plate from the freezer, press a doubled 12-inch piece of heavy-duty foil inside the pie shell, and fold the edges of the foil to shield the fluted edge; distribute 2 cups ceramic or metal pie weights over the foil. Bake, leaving the foil and weights in place until the dough looks dry and is light in color, 25 to 30 minutes. Carefully remove the foil and weights by gathering the corners of the foil and pulling up and out. For a partially baked crust, continue baking until light golden brown, 5 to 6 minutes; for a fully baked crust, continue baking until deep golden brown, about 12 minutes more. Transfer to a wire rack.