Cider-Caramel Apple Pie

1. Roll out one disk of dough and fit it into a 9-inch pie pan. Roll out the second disk as directed in Cook's Note and place on a parchment-lined baking sheet. Chill the crusts while you prepare the caramel and filling.
2. Make the caramel: In a large wide pot, bring the cider to a boil over medium heat, then lower to medium-low heat and cook, without stirring, until the cider reduces to a sauce with the consistency of thin caramel, 45 to 60 minutes (the timing will depend on the size of your pot; check the progress every 15 minutes or so to start, and more frequently once it begins to thicken). 
3. Stir the butter, salt, and vanilla into the caramel, then pour the mixture into a heatproof bowl to cool slightly, about 15 minutes. 
4. Make the filling: Place the apples in a large bowl. In a small bowl, stir the brown sugar, flour, and cinnamon together. Add the mixture to the apples and toss to coat. Add the cooled caramel and toss well to combine. 
5. Arrange the filling in the chilled piecrust: If you place the apples in overlapping concentric circles, like a rosette, there will be fewer air pockets between the fruit, reducing the chance of the top crust collapsing after baking. Once you reach the upper edge of the pie pan, begin to make the circles smaller to mound the filling higher in the center to give the baked pie the domed look. 
6. Roll up the top crust onto the rolling pin and gently unfurl it over the filling. Press the edges of the top and bottom crusts gently together to seal, then trim the excess dough away using scissors, leaving a 1/2-inch overhang. Tuck the overhang under itself all the way around the pie. 
7. Crimp the edges of the crust as desired. I refrigerate the pie for 20 to 30 minutes. 
8. Preheat the oven to 425 degrees F (218 degrees C), preferably with a baking stone on the bottom rack. 
9. Brush the top crust with the egg wash and sprinkle generously with turbinado sugar. Use a small sharp knife to cut a few small vents in the crust. Bake the pie on the stone or bottom rack until the crust is deeply golden and the filling is bubbling up through the vents, 40 to 50 minutes. If the crust begins to brown too quickly, reduce the oven temperature to 375 degrees F (190 degrees C) and/or tent the crust or edges with foil. Cool the pie for at least 30 minutes before serving. 

Egg wash:

1. To mix the dough by hand: In a large bowl, whisk together the flour and salt. Add the butter cubes, tossing them through the flour until each piece is well coated. Cut the butter into the flour by pressing the pieces between your palms or your fingers, flattening the cubes into big shards and continuing to toss them through the flour, recoating the shingled pieces.
2. For a flaky crust, continue cutting the butter into the flour just until the pieces of butter are about the size of walnut halves. Or, for a mealy crust, continue to work the mixture together until the pieces of butter are about the size of peas. To mix the dough in a food processor: See Pro Tip. 
3. Make a well in the center of the flour mixture. Add 3 tablespoons ice water for a single crust or 6 tablespoons for a double crust and mix to incorporate. Then add more ice water 1 tablespoon at a time and continue mixing just until the dough comes together. As it begins to come together, you can knead it a few times to make sure it's fully combined. It's important not to add too much water to the dough, which should never be sticky— it should hold together easily in a ball but still feel almost dry to the touch. 
4. Form the dough into an even disk if making a single crust; or divide in half and shape into 2 equal disks if making a double crust. Wrap tightly in plastic wrap and chill for at least 30 minutes or up to overnight.  
5. For a double-crust pie: Using one disk of dough, follow the instructions for a single-crust pie and chill the bottom crust in the pie pan. Roll out the second disk of dough on a lightly floured surface to 1/4-inch thick and place on a parchment-lined baking sheet. Chill in the refrigerator for 10 to 15 minutes. 
6. Fill the bottom crust as directed in the recipe. Roll the top crust up onto the rolling pin, starting at the far edge of the dough. With the pie pan in front of you, start at the edge closest to you and gently unfurl the dough onto the filling. Trim the excess dough from the edges, leaving a 1/2-inch overhang all around. Use your fingers to press the edges of the bottom and top crusts together so they are lightly sealed. Chill the pie in the refrigerator for 15 to 30 minutes or freeze for 5 minutes. 
7. Tuck the excess dough under at the edges, pressing lightly to help seal the dough to the rim of the pie pan. Return the dough to the refrigerator for 15 to 30 minutes or to the freezer for 5 to 10 minutes. Crimp the edges of the piecrust as desired. Bake as directed in the recipe.