Make the pie dough: Add 1 1/2 cups flour, salt and sugar to the bowl of an electric food processor. Pulse until just combined, about two 1-second pulses. Add the butter and the shortening. Process until the dough is begins to collect in uneven clumps resembling cheese curds, and there is no uncoated flour, about 15 seconds. Scrape down the sides of the bowl with a rubber spatula, then add the remaining 1 cup of flour. Pulse until the mixture is evenly distributed, and the dough is evenly broken up, about 5-6 quick pulses. Transfer the mixture into a medium-sized mixing bowl.
Sprinkle the vodka and water over the mixture. Using a rubber spatula, fold the mixture together, until the dough is slightly tacky and sticks together. Divide the dough into two even balls, and flatten each into a 4-inch disk. Wrap each separately in plastic wrap. Refrigerate at least 45 minutes, and up to 2 days.
Remove one disk of dough from the refrigerator. On a generously floured work surface, roll out the dough to a 12-inch circle, of about 1/8-inch thick. Roll the dough loosely onto the rolling pin, then lift it and unroll it into a 9-inch pie plate, leaving at least a 1-inch overhang around the edge. Gently press the dough into the pie plate bottom. Refrigerate while preparing the filling, or at least until the dough is firm, about 30 minutes.
Arrange an oven rack in the lowest position, place a rimmed baking sheet on the oven rack, and preheat oven to 400°F.
For the filling: Place 3 cups of blueberries in a medium saucepan set over medium heat. Using a potato masher, smash the berries several times (about 5-6 times) so they will begin to release their juices. Cook, stirring frequently and mashing occasionally, until the mixture is thickened and reduced to about 1 1/2 cups, and about half the berries have broken down, about 8-10 minutes. [If using frozen blueberries, cook half of the frozen berries over medium-high heat, stirring frequently and without mashing, until reduced to about 1 1/4 cups, 12-15 minutes.] Let cool slightly.
Place the grated apple in a thin, clean kitchen towel and wring dry. Transfer the apple grating to a large mixing bowl, and discard (or drink!) the juice. Add the cooked blueberries, the remaining 3 cups of uncooked blueberries, the lemon zest, lemon juice, 3/4 cups sugar, tapioca and salt. Stir to combine thoroughly. Transfer the mixture to the dough-lined pie plate. Evenly scatter the butter pieces over the berry filling.
Roll out the remaining disk of dough to a 11-inch circle, again about 1/8-inch thick, on a generously floured work surface. Using a 1-inch round circular biscuit cutter, cut a round from the center of the dough, then cut another 6 rounds, equally spaced around this center circle, each about 1/2-inch apart. Roll the dough loosely onto the rolling pin, then lift it and unroll it over the pie, leaving at least 1/2-inch overhang around the edges.
Using kitchen shears, trim the bottom layer of overhanging dough to a 1/2-inch overhand. Fold the overhang of the top dough over the edge of the bottom dough, so that the edge of the fold is flush with the outer rim of the pie plate. Flute the edges, or press with the back of a fork to seal. Brush the top and edges of the pie crust with the egg-water mixture. Sprinkle evenly with the remaining tablespoon of sugar. If the dough seems very soft, place in the refrigerator for about 15 minutes.
Place the pie on the heated baking sheet. Bake 30 minutes, then reduce the heat to 350 F and continue to bake until the crust is deeply golden brown and the blueberry juices bubble, about 30-40 minutes more. Transfer the pie to a wire rack and cool to room temperature, about 4 hours. Cut into wedges and serve, preferable with vanilla ice cream.