Make the crust: Pulse the flour, granulated sugar and salt in a food processor until combined. Add the shortening and pulse a few times until the mixture looks like coarse meal. Add the butter and pulse a few times until it is in pea-size pieces. Add the ice water and vodka; pulse a few times until the dough starts coming together but is still crumbly. Turn out onto a sheet of plastic wrap and form into a disk. Wrap and refrigerate until firm, at least 1 hour or overnight.
Meanwhile, make the topping: Combine the oats, flour, brown sugar, salt, allspice and ginger in a medium bowl. Using your fingers, work the butter into the mixture until clumpy. Refrigerate until ready to use.
Put a baking sheet in the lower third of the oven; preheat to 400 degrees F. Make the filling: Combine the strawberries, brown sugar, granulated sugar, tapioca, lime juice, cardamom and salt in a large bowl. Stir until the sugar and tapioca are dissolved and the strawberries are evenly coated. Set aside.
Roll out the dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch pie plate. Fold the overhanging dough under itself and crimp the edges with your fingers or a fork. Refrigerate until firm, at least 15 minutes. Spread the strawberry filling in the crust and sprinkle evenly with the crumble topping. Place the pie on the hot baking sheet and bake until the crust is golden brown and the juices are bubbling around the edge, about 1 hour. Transfer to a rack and let cool completely, at least 4 hours.