For the Pie Dough
In a large liquid measuring cup, whisk together the water and vinegar. Add the ice and whisk. Refrigerate while you prep the rest of the ingredients.
Slice the butter into 1-inch cubes, placing the cubes in a small bowl as you go. Freeze while you prep the rest of the ingredients.
Combine the flour, sugar, and salt in a food processor. Pulse to combine. Add the frozen butter and pulse until the dough starts to resemble coarse meal, with pea-sized pieces of butter.
Remove the ice mixture from the refrigerator. Add 6 tablespoons of the mixture one at a time, pulsing for a few seconds after each addition. Scoop up a small handful of dough and pinch—if the dough holds together once pinched, it's time for the next step. If it still feels crumbly and dry, keep adding water from the ice mixture, 1 teaspoon at a time, until the dough holds when pinched.
Tip the dough into a large bowl and use your hands to squeeze it together and quickly knead it into a rough ball. Use a bench scraper to divide the dough into two halves, each around 11 ounces in weight. Shape each half into a rough ball. Wrap each portion tightly in plastic wrap and flatten each into a small disc. Refrigerate for at least 1 hour, preferably overnight. The dough will keep in the refrigerator for up to 3 days, and in the freezer for up to 3 months.
For the Tayberry Pie Filling
In a medium, heavy-bottomed sauce pot, combine 2 1/2 cups of the tayberries with the sugar, cornstarch, lemon juice, and salt. Cook, over medium heat, until the cornstarch has dissolved and the mixture has thickened considerably, around 15 minutes. Remove from heat and stir in the remaining 2 cups of tayberries.
Remove one of the dough discs from the refrigerator and place on a lightly floured surface. Use a rolling pin to roll it into a 10- to 11-inch circle. If the dough is too hard to roll out, give it a few whacks with your rolling pin, rotating the disc after every whack to ensure that it's flattening evenly. Transfer the dough circle onto your pie plate to make the bottom crust. Use a rubber spatula to scrape the tayberry pie filling into the bottom crust, spreading the filling evenly across the pan. Refrigerate while you work with the second disc of dough.
Remove the second dough disc from the refrigerator and follow the instructions above to roll it into a 10- to 11-inch circle. Transfer the dough circle onto a parchment paper-lined sheet pan and freeze for 5 minutes. After 5 minutes, use star-shaped cookie cutters to stamp out stars in the dough, taking care to stamp in the center of the pie and leave a 2-inch border clear for the crust. Freeze once more for 5 minutes.
Remove the top crust from the freezer and carefully transfer to the bottom crust, centering over the filling. Use kitchen shears to trim off any dough overhanging over the edge of the pie plate, leaving 1 inch of overhang. Fold the overhanging dough onto itself, aligning the edge of the dough to the inner edge of the pie pan. Pinch along the fold all the way around to create a crimp. Dust your fingers with flour. Take your thumb and press it into the folded overhang, using your thumb and index finger on the opposite hang to pinch around your thumb and create a crimp. Repeat, crimping the dough around the entire pan, flouring your hands as necessary to prevent the dough from sticking. Cover loosely with plastic wrap and freeze for 4 hours, preferably overnight.
Once the pie is frozen solid, position a rack in the lower-third of the oven and preheat to 375 (F). Line a sheet pan with parchment paper. Make an egg wash by whisking together the remaining egg white and water.
Remove the pie from the freezer and place on the center of the sheet pan. Working quickly, use a pastry brush to brush the top of the pie with the egg wash, avoiding brushing the crimp. Bake in the preheated oven for 60 to 70 minutes, or until the fruit filling is bubbling slowly in the center. Cool completely on a wire rack. The pie will keep at room temperature, under a cake dome or a large bowl turned upside down, for up to 1 day. After 1 day, cover loosely with plastic wrap and refrigerate for up to 2 more days.