To make the crust: Stir the flour, salt, and sugar together in a large bowl. Add the butter pieces and coat with the flour mixture using a bench scraper or spatula. With a pastry blender, cut the butter into the flour mixture, working quickly until mostly pea-size pieces of butter remain (a few larger pieces are okay; be careful not to overblend).
Combine the water, cider vinegar, and ice in a large measuring cup or small bowl. Sprinkle 2 tablespoons of the ice water mixture over the flour mixture, and mix and cut it in with a bench scraper or spatula until it is fully incorporated. Add more of the ice water mixture, 1 to 2 tablespoons at a time, using the bench scraper or your hands (or both) to mix until the dough comes together in a ball, with some dry bits remaining. Squeeze and pinch with your fingertips to bring all the dough together, sprinkling dry bits with more small drops of the ice water mixture, if necessary, to combine.
Divide the dough in half and shape the dough into flat discs, wrap in plastic, and refrigerate for at least 1 hour, preferably overnight, to give the crust time to mellow. Wrapped tightly, the dough can be refrigerated for 3 days or frozen for 1 month.
Remove the dough from the fridge 5 to 10 minutes before you being rolling. Dough that is too cold will develop cracks when it is rolled.
Lightly flour your work surface and roll out one of the discs of dough until it is 2 to 3 inches larger than the pan you are using and about 1/8 inch in thickness. Fold the dough in half and lay it across one side of a well-buttered pie pan (no need to butter if you are using a ceramic pie dish), positioning the seam in the center. Unfold the disc and gently slide and fit the dough down into the pan; do not pull or stretch the dough. Make sure there are no gaps between the dough and the pan; if there are air bubbles, burst them with a fork.
Trim the dough overhang to allow 1 to 1 1/2 inches of excess, measuring from the inner rim of the pan. Cover the crust with plastic and refrigerate for at least 30 minutes, preferably 1 hour or more, and tightly wrapped, up to 3 days before using. The rolled out, fitted, tightly wrapped crust can also be frozen for up to a month.
On a lightly floured surface, roll out the other disc of dough into a circle approximately 12 inches in diameter and about 1/8 inch thick. To cover pie with a pastry round, simply place dough round on a parchment lined pan and chill for a minimum of 30 minutes. If making a lattice top, use a pizza cutter or fluted pastry wheel to trim one inch of dough from either side of the circle, and then cut the remaining shape into 8 strips of equal width (this will result in a 4-by-4 lattice–you can cut from 12 to 18 thinner strips and create a 6-by-6 or 9-by-9 lattice respectively, depending on your preference of lattice style). Transfer the lattice strips to a parchment lined pan and chill for a minimum of 30 minutes.
For the filling: Have ready and refrigerated one pastry-lined 9-inch pie pan and pastry round or lattice to top.
Juice the lemon and orange into a large bowl, removing any seeds. Prepare the pears using an apple-peeling machine, or core, peel, and thinly slice them with a sharp knife or on a mandoline until you have about 5 cups sliced. Dredge the slices in the lemon and orange juice. Sprinkle lightly with 2 tablespoons of the granulated sugar. Set aside to soften slightly and release some of the juices, 20 to 30 minutes.
In the bowl of a food processor fitted with the blade attachment, combine the remaining 1/2 cup granulated sugar, flour, juniper berries, cinnamon, salt, and lemon zest; process until the juniper berries are chopped and fragrant. To remove any remaining large pieces of juniper berry, shake the sugar mixture through a fine-mesh sieve into a large bowl.
Leaving behind any excess juice, transfer the pears to the bowl together with the sugar mixture, add the honey, and toss to combine. Tightly layer the pears in the prepared pie shell so that there are minimal gaps, mounding them slightly higher in the center. Arrange the lattice or pastry round on top and crimp as desired.
Chill the pie in the refrigerator for 10 to 15 minutes to set the pastry. Meanwhile, position the oven racks in the bottom and center positions, place a rimmed baking sheet on the bottom rack, and preheat the oven to 425°F.
Brush the pastry with the egg wash to coat, and sprinkle with the desired amount of demerara sugar. Place the pie on the rimmed baking sheet on the lowest rack of the oven. Bake for 20 to 25 minutes, or until the pastry is set and beginning to brown.
Lower the oven temperature to 375°F, move the pie to the center oven rack, and continue to bake until the pastry is a deep golden brown and the juices are bubbling, 30 to 35 minutes longer. Test the pears with a skewer or sharp knife; they should be tender.
Allow to cool completely on a wire rack, 2 to 3 hours. Serve slightly warm or at room temperature.
The pie will keep refrigerated for 3 days or at room temperature for 2 days.