Make the crust: Pulse the flour, granulated sugar, salt, cinnamon, ginger, cardamom, nutmeg and allspice in a food processor to combine. Add the butter; pulse several times until it looks like coarse meal. Add the vinegar and 1/4 cup ice water; pulse a few more times until the dough comes together and forms a ball. Turn the dough out onto a piece of plastic wrap; press into a disk and wrap. Refrigerate until firm, at least 1 hour or overnight.
Roll out the dough into a 12-inch round on a lightly floured surface. Ease into a 9-inch pie plate, pressing the dough into the bottom and up the side. Fold the overhanging dough under itself and crimp with your fingers or a fork. Freeze until firm, about 1 hour.
Put a baking sheet on the middle oven rack and preheat to 375 degrees F. Line the crust with foil, then fill with pie weights or dried beans. Transfer to the hot baking sheet and bake until lightly golden around the edge, about 20 minutes. Remove the foil and weights and continue baking until the crust is golden all over, about 10 more minutes. Transfer to a rack and let cool completely; leave the baking sheet in the oven.
Meanwhile, make the filling: Whisk the pumpkin puree, eggs, heavy cream, granulated sugar, vanilla, cinnamon, ginger, cardamom, nutmeg, allspice and salt in a medium bowl until well combined. Pour into the cooled crust and return to the hot baking sheet in the oven. Bake until set around the edge but the center still jiggles slightly, 50 minutes to 1 hour. Transfer to the rack and let cool completely.
Make the whipped cream: Beat the heavy cream, brown sugar, vanilla and cinnamon in a large bowl with a mixer on medium-high speed until soft peaks form, 2 to 3 minutes. Serve the pie with the whipped cream.