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To make the sourdough pie crust: Weigh your flours; or measure them by gently spooning them into a cup, then sweeping off any excess.
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In a large bowl, whisk together the flours, sugar, and salt. Place the bowl in the freezer until the mixture is cold, about 10 minutes. This step ensures the flakiest final crust.
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While the dry ingredients chill, dice the cold butter into small cubes, or cut it into pats.
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Using a pastry blender, bowl scraper, or your fingertips, work the butter into the chilled dry ingredients, pressing the pieces to flatten them into flakes about the size of quarters (1" in diameter).
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Make a well in the center of the mixture and pour in the sourdough starter, beginning with the lower amount (1/2 cup or 113g). Using a bowl scraper, mix in the sourdough. Initially, it will be difficult to combine the ingredients; this is normal. Continue to mix the ingredients in the bowl, using pressing and folding motions, until the dough starts to become cohesive. If the dough remains dry and doesn’t come together after a few minutes, add the remaining portion of sourdough (1 generous tablespoon or 20g).
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Transfer the dough and any remaining bits in the bowl to a clean work surface and press them together with the palm of your hand.
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When most of the dry bits are incorporated, lightly flour your work surface, then gently press or roll the dough into a disk about 1/2" thick or 6" to 7" in diameter. Cover and chill the dough for at least 20 minutes and up to 2 days.
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When ready to bake, preheat the oven to 425°F and position a rack in the center. If you have one, place a baking steel or stone on the rack. (See “tips,” below.)
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Roll out the chilled dough to a 13" round, transfer to a 9" metal pie pan, and crimp the edges (see "tips" below if baking in a non-metal pan). Refrigerate while you prepare the filling and topping.
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To make the apple filling: In a large bowl, combine the apples, boiled cider, and lemon juice. Stir gently with a flexible spatula to coat the apples.
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In a small bowl, whisk together the sugar, flour, cinnamon, and salt. Sprinkle the mixture over the apples and stir to coat.
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To make the topping: In a medium bowl, whisk together the flour, sugar, cinnamon, and salt. Add the butter and toss to combine. Using a bowl scraper, fork, or your fingers, work in the butter until crumbs form and no dry spots remain.
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To assemble the pie: Remove the pie pan from the refrigerator and spoon the apple filling into the pan. Press down to compact the apples into an even, tightly packed dome. Sprinkle the topping evenly over the apples.
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Place the pie on a parchment-lined baking sheet to catch any drips, then place the baking sheet directly on the preheated steel or stone. Bake at 425°F for 15 minutes.
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Reduce the heat to 350°F and bake for an additional 60 to 75 minutes, checking after 45 minutes to see if the edges are browning too quickly. (If necessary, cover the edges with foil or a pie shield.) The pie is done when the filling is bubbling vigorously around the edges.
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Remove the sourdough apple pie from the oven and let it cool completely before slicing. If desired, dust the pie with non-melting sugar before slicing and serving.
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Storage information: Store any leftover sourdough apple pie, covered, at room temperature for several days; freeze for longer storage.