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1
Pie Dough: In the bowl of a food processor, process 1 1/2 cups flour, salt, and sugar until combined. Add butter and shortening and process for about 15 seconds or just until dough starts to collect in uneven clumps (dough should look like cottage cheese curds and there should be no uncoated flour). Scrape bowl of processor to redistribute dough evenly. Add remaining flour and pulse 4 to 6 times or until mixture is evenly distributed around bowl and dough has been broken up.
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2
Transfer dough into a medium bowl. Sprinkle vodka and water over dough. Using a rubber spatula and a folding motion, press down on dough until it is slightly tacky and sticks together. Divide dough in half and flatten into 4 inch disks. Wrap each in plastic wrap and refrigerate at least 45 minutes (up to 2 days).
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3
Remove 1 disk of dough from fridge and roll out on a lightly floured surface into a 12 inch circle. Roll dough loosely around rolling pin and unroll it into a pie plate (leaving a 1 inch overhang on each side). Lightly press dough into pie plate; refrigerate while preparing berry filling.
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4
Filling:
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5
Adjust oven rack to lowest position, place baking sheet on oven rack, and heat oven to 400 degrees F.
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6
Meanwhile, place 1 cup of each of the three berries in a medium sized saucepan over medium heat. Using a potato masher (or something similar), mash berries several times to release juices. Continue to cook and stir frequently and mash occasionally, until half the berries have broken down and mixture has thickened and reduced (about 8 minutes). Then remove it from the heat and allow to cool slightly.
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7
Place grated apple in a clean kitchen towel and wring it dry. Transfer apple to large bowl, add cooked berries, uncooked berries, lemon juice, sugar, tapioca, and salt; toss to combine. Transfer mixture to the dough-lined pie plate and scatter butter pieces over filling.
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8
Roll out the second piece of pie dough into another 12 inch circle. With a pastry wheel (or pizza cutter or knife), cut dough into 12 strips, each about 3/4 inch wide. Place 6 strips horizontally across the top of the pie every 1 inch. Weave in the remaining 6 strips. Fold dough under itself so that the edge is flush to the outside rim of the pie plate. Flute the edges or use a fork to seal pie crusts together. Brush top and edges of pie with egg mixture. If dough is soft, chill for 10 minutes in freezer.
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9
Place pie pan on a heated baking sheet and bake 30 minutes at 400 degrees F. Then reduce oven to 350F and continue baking for another 40 to 45 minutes, or until juices bubble and crust is golden brown.
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10
Transfer pie to a wire rack; cool to room temperature (at least 4 hours-this is the hardest part... but very crucial. Don't skimp on the cooling time!). Cut into wedges and serve with your favorite ice cream!
