Whisk the pastry flour and sugar together in a large mixing bowl. Slice each stick of butter into about 12 pieces. Toss the butter into the flour and place the bowl in the freezer for 30 minutes. Combine the vinegar and water and place in the refrigerator for 30 minutes.
Remove the bowl from the freezer and dump the contents on to the counter. Using a rolling pin, flatten/smear the butter into the flour (I recommend using a rolling pin to fraisage the dough). Your goal is sheets of butter, crumbly bits of butter/flour and almost no loose flour. Use a bench scraper to move the dough around as you work, periodically bringing it all back into a pile in front of you. Break up any large sheets of butter with your fingers so all the butter bits are relatively uniformly shaped.
Once your pile consists of butter sheets and crumbly dough, sprinkle a little of the cider/water mixture over your pile and use your hands to gently incorporate the liquid into the flour and butter (I kind of toss the dough around in my hands and move it around a bit on the counter with the bench scraper). Continue sprinkling and incorporating until the dough is uniform - about 4 sprinkles in total.
Form the dough into a ball, as best you can, and transfer the dough to a sheet of plastic wrap. Use the plastic wrap to mold the dough into a disc. Wrap it tightly and place it in the refrigerator for at least 30 minutes.
Lightly flour a work surface, remove the disc from the fridge, and place it on the surface. Flour the top of the disc, and let it rest on the counter until it softens a bit — about 10 minutes, or so.
Using your rolling pin (and your fingers, if necessary) begin rolling/molding the dough into the shape of a rectangle. Sprinkle extra flour on the disc and your work surface to combat the stickiness, if needed.
Once in the shape of a rectangle, take one of the ends of the rectangle and fold it a little more than halfway across the rectangle toward its other end. Then take the other end and fold that over the first (as if you are folding a long and skinny "business" letter).
Once the dough is folded, roll it out again into a rectangle (re-flouring beneath it and on top, if necessary), and fold up the ends, like a letter, for a second time. Repeat this one or two more times (3 to 4 times in total). By the third time, your dough should have transformed into something much more pliable and easier to work with. Cut the final rectangle in half, form each half into a disc (or keep it in its rectangular shape, if making a slab pie), tightly wrap each disc/rectangle in plastic wrap, and place in the refrigerator for 45 minutes.
Remove one disc/rectangle from the refrigerator, roll it out, generously flouring your work surface as you go, and place it in the bottom of your pie plate or 1/4 sheet pan (or half sheet pan if making a large slab pie). Patch any holes with a bit of extra dough. Place the rolled-out dough back in the refrigerator. Prepare your filling. Remove the pie dish/pan from the fridge and fill it. Take out the second disc/rectangle, roll it out, and cover your filling with the second rolled-out disc, crimp the edges, and using a paring knife make several cuts in a decorative pattern on the top of the pie (if making a slab pie, use a fork to decoratively puncture the top of the pie).
In a small bowl, whisk the egg and cream together and, using a pastry brush, brush the top of the pie with the egg wash. Sprinkle sugar in the raw over the pie and place in the freezer for one hour (freezing the pie before baking it prevents shrinkage).
Preheat the oven to 425 degrees F and bake the pie for 45 to 50 minutes, or until the juices are bubbling through the vents (a slab pie will bake in less time — more like 35 to 40 minutes).