For the Baked Pie Shell:
1¼ cups all-purpose flour
½ teaspoon salt
1 tablespoon sugar
6 tablespoons cold unsalted butter, cut into ¼-inch slices
¼ cup chilled vegetable shortening, cut into 4 pieces
¼ cup ice water
For the Filling:
4 pints (about 3 pounds) fresh strawberries, gently rinsed and dried, hulled
¾ cup granulated sugar
2 tablespoons cornstarch
1½ teaspoons Sure-Jell for low-sugar recipes (the pink box)
Pinch of salt
1 tablespoon lemon juice
1. Make the Pie Crust: Process ¾ cup flour, salt and sugar together in food processor until combined, about two 1-second pulses. Add butter and shortening and process until homogenous dough just starts to collect in uneven clumps, about 10 seconds (dough will resemble cottage cheese curds with some very small pieces of butter remaining, but there should be no uncoated flour). Scrap down sides and bottom of bowl with rubber spatula and redistribute dough evenly around processor blade. Add ½ cup flour and pulse until mixture is evenly distributed around bowl and mass of dough has been broken up, 4 to 6 quick pulses. Empty mixture into a medium bowl.
2. Sprinkle the water over the mixture. With a rubber spatula, use a folding motion to mix, pressing down on dough until dough is slightly tacky and sticks together. Flatten dough into a 4-inch disk. Wrap in plastic wrap and refrigerate at least 45 minutes or up to 2 days.
3. Adjust oven rack to lowest position and preheat oven to 425 degrees F. Remove dough from refrigerator and roll out on generously floured work surface to 12-inch circle about 1/8-inch thick. Roll dough loosely around a rolling pin and unroll into pie plate, leaving at least 1-inch overhang on each side. Working around circumference, ease dough into plate by gently lifting edge of dough with 1 hand while pressing into plate bottom with other hand. Leave overhanging dough in place; refrigerate until dough is firm, about 30 minutes.
4. Trim overhang to ½ inch beyond lip of pie plate. Fold overhang under itself; folded edge should be flush with edge of pie plate. Flute dough or press tines of fork against dough to flatten against rim of pie plate. Refrigerate dough-lined plate until firm, about 15 minutes.
5. Remove pie plate from refrigerator and use a fork to prick the bottom of the dough. Line the crust with foil, and fill with pie weights or dried beans. Bake for 15 minutes. Remove foil and weight, rotate plate, and bake for 5 to 10 additional minutes, until crust is golden brown and crisp. Let cool to room temperature.
6. Make the Filling: Select 6 ounces misshapen, underripe, or otherwise unattractive berries, halving those that are large; you should have about 1½ cups. In a food processor, process the berries to a smooth puree, 20 to 30 seconds, scraping down the bowl as needed.
7. Whisk the sugar, cornstarch, Sure-Jell, and salt in a medium saucepan. Stir in the berry puree, making sure to scrape the corners of the pan. Cook over medium-high heat, stirring constantly with a heatproof rubber spatula, and bring to a full boil. Boil, scraping the bottom and sides of the pan to prevent scorching, for 2 minutes to ensure that the cornstarch is fully cooked (mixture will appear frothy when it first reaches a boil, then will darken and thicken with further cooking). Transfer to a large bowl and stir in lemon juice. Let cool to room temperature.
8. Meanwhile, pick over the remaining berries and measure out 2 pounds of the most attractive ones; halve only extra-large berries. Add the berries to the bowl with the glaze and fold gently with a rubber spatula until the berries are evenly coated. Scoop the berries into the pie shell, piling into a mound. If any cut sides face up on top, turn them face down. If necessary, rearrange the berries so that holes are filled and the mound looks attractive. Refrigerate pie until chilled, about 2 hours. Serve within 5 hours of chilling.