for the crust:

1. Sift the flour, salt, and sugar together in a food processor. Add the butter pieces and shredded cheese and pulse briefly, until you achieve pea-sized pieces of butter. Careful not to over mix.
2. Combine the water, cider vinegar, and ice in a small bowl. Sprinkle 2 tablespoons of this ice water mixture over the flour mixture, and pulse until it is fully incorporated. Add more of the ice water mixture, 1 to 2 tablespoons at a time until the dough comes together in a ball. Take the dough out of the processor at this point and work the dough with your hands, adding small drops of the ice water mixture as you see fit, until it’s all combined. Work the dough until just combined. You should see faint marble ribbons of butter in your dough.  
3. Then divide the dough into two flat discs and wrap tightly in plastic wrap. Let them sit for at least one hour, but preferably over night, in the refrigerator.
4. tip! If wrapped tightly, the dough can be refrigerated for 3 days or frozen for 1 month.

for the filling:

1. Melt butter in a large sauté pan over medium-high heat and add your apples to the pan. Stir to coat the apples with butter and cook for a few minutes, stirring occasionally. While the apples cook, whisk together the cinnamon, salt and ¾ cup sugar and then sprinkle this mixture over the apples, stirring to combine.
2. Lower your heat and continue to cook the apples until they start to soften, about 5 to 7 minutes. (Your house should smell amazing at this point.) Sprinkle the flour and tapioca (or corn) starch over the apples and continue to cook, stirring occasionally, for another 3 to 5 minutes.
3. Remove pan from heat, add cider vinegar, stir and scrape apple mixture into a bowl and allow to cool completely. I made my filling one day ahead of time, stored it in the refrigerator and then brought it to room temperature the next day before placing it in the pie shell. 

To bake: 

1. Place a large baking sheet on the middle rack of oven and preheat to 425° F / 220° C. Take one disc of dough from the refrigerator and roll it out with a rolling pin on a lightly floured surface until it is roughly 12 inches / 30cm in diameter. Fit this crust into a 9-inch pie dish, pressing down so there are no air bubbles. Crimp and form the edges of your pie with the overhanging dough and pop pie shell in the freezer for about 5-10 mins. Take the pie out of the freezer and fill with your cooled filling. Set aside.
2. Roll out the remaining dough (this is the top of the pie) on a lightly floured surface until it is roughly 10 or 11 inches / 25 or 28cm in diameter. Cut this dough however you’d like (I chose to make a lattice) laying your design over the pie filling and pressing the edges of the top of your pie crust with the bottom of the pie crust with your fingers. Make sure your pie crust top has a way for steam to escape - so if it’s a solid top, cut a few slits in the top.
3. Lightly brush the top of the pie with egg wash and sprinkle with turbinado sugar.
4. Place pie in the oven, on the hot baking sheet and bake for 20 minutes. Then reduce temperature to 375° F / 190° C. Cover pie with a loose tent of tin foil to prevent over-browning and continue to cook until the interior of the pie is bubbling and the crust is golden brown, about 30 to 40 minutes more.
5. Allow the pie to cool for about 2 hours before cutting and serving. (If you can wait that long.)  Serve warm with vanilla ice cream and a generous wedge of cheddar cheese.