For the pie dough:

1. Process flour, salt, and sugar together in food processor until combined, about 3 seconds. Add butter and pulse until butter is size of large peas, about ten 1-second pulses.
2. Using fork, mix sour cream and 1/3 cup ice water in small bowl until combined. Add half of sour cream mixture to flour mixture; pulse for three 1-second pulses. Repeat with remaining sour cream mixture. Pinch dough with fingers; if dough is floury, dry, and does not hold together, add 1 to 2 tablespoons ice water and process until dough forms large clumps and no dry flour remains, three to five 1-second pulses. Dough should feel a little like Play-doh, as a reference.
3. Turn dough out onto work surface. Divide dough into 2 balls and flatten each into 4-inch disk; LIGHTLY dust with a little flour, then wrap each disk in plastic and refrigerate until firm but not hard, 1 to 2 hours (or at least a half hour), before rolling. (Dough can be refrigerated for up to 24 hours. Let thoroughly chilled dough stand at room temperature for 15 minutes before rolling.)
4. Place empty rimmed baking sheet on the lowest oven rack, and heat oven to 425 degrees.

For pie filling:

1. Peel, core, and cut apples into 1/2-to-3/4-inch slices and toss with 3/4 cup sugar, lemon juice, allspice, cinnamon and pinch of salt. Toss apple mixture together until evenly coated. Transfer apples to a colander or strainer, over a large bowl and allow the apple liquid to drain for at least 30 minutes. You should be left with about 1 cup of juice. Pour the leftover apple liquid into a microwave-safe glass measuring cup or bowl, and microwave on High until the liquid has reduced by about half. You should have about 1/3 cup of reduced apple liquid. Set aside while you prepare the rest of the pie.
2. Remove 1 disk of dough from refrigerator and roll out between 2 large sheets of parchment paper or plastic wrap to 12-inch circle, about 1/8 inch thick. (If dough becomes soft and/or sticky, return to refrigerator until firm.) Remove parchment from one side of dough and flip onto 9-inch pie plate; peel off second layer of parchment. Working around circumference, ease dough into plate by gently lifting edge of dough with one hand while pressing into plate bottom with other hand. Leave dough that overhangs plate in place; refrigerate until dough is firm, about 15 minutes.
3. Meanwhile, roll second disk of dough between 2 large sheets of parchment paper or plastic wrap to 12-inch circle, about 1/8 inch thick. Refrigerate, leaving dough between parchment sheets, until firm, about 15 minutes.
4. Toss the apples evenly with 1 to 2 tablespoons of cornstarch. Fill the bottom portion of the pie with the apple mixture, and drizzle the reduced apple liquid all over the filling; it will almost immediately harden, but don’t worry. It will melt again once it’s baked. Remove parchment from one side of remaining dough and flip dough onto apples; peel off second piece of parchment. Pinch edges of top and bottom dough rounds firmly together. Trim excess dough with kitchen shears, leaving 3/4-inch overhang. Fold dough under itself so that edge of fold is flush with outer rim of pie plate. To seal pie, flute edges using thumb and forefinger or press with fork. Brush surface with beaten egg white and sprinkle evenly with remaining teaspoon sugar.
5. Set pie on preheated baking sheet; bake until crust is a deep golden brown, 40 to 55 minutes. Transfer pie to wire rack and cool at least 2 to 3 hours before cutting into it.