Make the crust: Combine the flour, granulated sugar and salt in a food processor and pulse to combine. Add the shortening and pulse until it looks like cornmeal. Add the butter and pulse a few times until the butter is in pea-size pieces. Add the vinegar and 1 tablespoon ice water; pulse until the dough starts coming together but is still crumbly, adding 1 more tablespoon ice water if necessary. Turn the dough out onto a piece of plastic wrap; shape into a disk and wrap. Refrigerate until firm, at least 1 hour or overnight.
Put a baking sheet on the middle oven rack and preheat to 425 degrees F. Meanwhile, 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 with your fingers or a fork. Refrigerate until firm, at least 30 minutes.
Meanwhile, make the filling: Whisk the eggs, brown sugar, corn syrup, melted butter, bourbon, vanilla, salt, walnuts and chocolate chips in a large bowl until smooth. Pour the filling into the crust. Carefully place the pie plate on the hot baking sheet in the oven and reduce the temperature to 350 degrees F. Bake until the crust is golden and the filling is set around the edge but slightly jiggly in the center, 50 to 55 minutes. Transfer to a rack and let cool completely, 3 to 4 hours.