In the bowl of a food processor, process the flour, salt, and sugar until combined, about 3 seconds. Add the butter and pulse until butter is the size of small peas, about ten 1-second pulses. In a small bowl, whisk together the sour cream and ice water. Add half the sour cream to the flour and pulse briefly.  Repeat with the remaining sour cream mixture. Pinch the dough with fingers, if the dough is dry and does not hold together, add 1-2 tablespoons of ice water and process until large clumps form, about three to five 1-second pulses. Turn the dough out onto a work surface and press to combine lightly. Divide the dough in half, pressing each half into a flat disk, and wrap tightly in plastic wrap. Refrigerate until firm, at least 1 hour, preferably several hours, or for up to 2 days before using. The pastry can also be wrapped airtight, placed in a freezer bag and frozen for up to 6 months. Thaw completely in the refrigerator before using.

In a medium bowl, combine sugars, salt, zest, juice and cinnamon.  In a large dutch oven over high heat, melt the butter. Add the apples and toss until the apple slices are coated with butter. Reduce the heat to medium, cover tightly, and cook, stirring frequently until the apples are slightly softened, about 7-10 minutes. Add the sugar mixture and increase the heat to high. Cook the apples at a rapid boil, stirring frequently and gently until the juices become very thick and syrupy, about 7-10 minutes more. Immediately spread the apples in a thin layer on a large baking sheet and allow to cool to room temperature. Position a rack on the lower third of the oven and preheat to 425ºF.

Meanwhile, remove one disk of pastry to a lightly floured work sheet of parchment paper. For the bottom crust, roll out pastry to a 13-inch circle  adding flour as needed. Transfer pastry to a baking sheet and refrigerate until the dough is firm, about 30 minutes. Roll the other half of the pastry for the top crust onto a separate sheet of lightly floured parchment paper into a 12-inch circle. Transfer to another baking sheet and refrigerate until firm, about 30 minutes. Once firm, invert 13-inch bottom pastry into a deep 9-inch pie plate; peel off parchment paper. Ease pastry into plate by gently lifting edge of dough with one hand and pressing into bottom edges of the pie plate with the other hand. Allow overhang to remain in place. Refrigerate until firm, about 20 minutes.

Pour the cooled apple mixture into the bottom crust. Brush the edge of the bottom crust with cold water. Flip the 12-inch top crust onto the apples and peel off the parchment. Seal the edge, trim slightly, fold edges under, and crimp or flute. Cut several steam vents and brush with the beaten egg white. In a small bowl, combine the sugar and cinnamon for the topping. Sprinkle the top of the pie evenly with the sugar mixture. Place the pie on a baking sheet and bake until deep golden brown and bubbling, about 50-60 minutes. If the top appears to be browning too quickly the last 15 minutes, place a sheet of aluminum foil on top (do not wrap) to prevent over browning. Transfer pie to a wire rack to cool completely, about 3 to 4 hours. Enjoy!