Make the crust: Pulse 1 1/2 cups of flour and salt together to combine. Add the butter and shortening and pulse for 15 seconds until mixture starts clumping. Add the last cup of flour and pulse 4-6 times until the mass of dough is broken up. Pour the mixture out into a large bowl and sprinkle in the water and vodka. Fold until combined and separate the mixture evenly onto two sheets of plastic wrap. Form each into a disc, wrap, and chill overnight.
Make the filling: Preheat the oven to 400 degrees F, adjust the oven rack to the lowest position, and put a baking sheet on the rack to preheat along with the oven. Cook 3 cups frozen whole strawberries in a medium saucepan over medium heat, stirring frequently, until many of the berries have broken down and the mixture is thickened and reduced to 1 1/2 cups, about 12-15 minutes. Let cool slightly. Place the grated apple in a clean kitchen towel and wring dry. Transfer the apple to large bowl and add the cooked berries, the remaining 3 cups of uncooked berries, sugar, tapioca, and salt; toss to combine.
Assemble and bake: Roll out one disk of pie dough on a floured surface (since this is a wet dough, you can use more flour. Keep a bench scraper handy.) until it’s about 2 inches larger than your pie plate or skillet (I used a 10-inch skillet, but you could use a 9-inch pie plate and it should still work fine) all around. Use your rolling pin to help you drape the dough into your pie plate or skillet, letting the excess dough hang over. Pour strawberry mixture into the crust and scatter the 2 tablespoons of butter pieces over it. Roll out the second disk of dough and drape it over the top of the pie. Trim excess dough to about 1/2 inch all around and fold the top crust under the bottom crust. Crimp the edges. Cut a vent in the top crust and brush all over with the egg wash.
Place the pie on the heated baking sheet and bake 30 minutes. Reduce oven temperature to 350 degrees and continue to bake until juices bubble and crust is deep golden brown, 30 to 40 minutes longer. Transfer the pie to a wire rack and cool to room temperature, at least 4 hours. Whisk together the glaze ingredients and drizzle it lightly over the pie (use about half of it and reserve the rest for drizzling over pieces). Add sprinkles. Cut into wedges and serve.