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To make dough, combine flour, salt, and sugar in the bowl of a food processor. Rough chop butter, and add to flour mixture by pulsing 5 or 6 times. Drizzle in the ice water, pulsing food processor 2 or 3 times or just until dough holds together.
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Turn dough out onto a lightly floured surface and gather into a ball. Flatten into a disc and wrap tightly with plastic wrap.
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Repeat for the second batch of dough.
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Chill both discs for 30 minutes, or more, in the refrigerator. Meanwhile prepare filling.
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Preheat oven to 400 degrees. Butter a 12 x 17 x 1-inch rimmed baking sheet and set aside.
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In a large bowl, fold together all filling ingredients (excluding egg white) and set aside.
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On a large, lightly floured surface, roll out one of the dough rounds into a 14 x 19-inch rectangle. Fold into quarters and unfold inside prepared baking pan. Leave any excess dough overhanging edge. Place in refrigerator while you roll out top layer.
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Roll out second disc into a rough 14 x 19-inch rectangle. Remove bottom crust from fridge, carefully spoon in and arrange the apple slices, and then cover with top crust. Fold the edge of bottom crust up around the top crust and crimp to seal the pie. Take the time here to make a well-sealed crust – it will help to seal in juices and make for a better-tasting pie.
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Working quickly, brush top crust with egg white, and then prick all over with a fork. Bake 45 - 55 minutes, or until filling is bubbling and crust is a light golden brown.
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Cool 2 hours, and then serve.