Preheat the oven to 350°F and line a couple of baking sheets with parchment paper.
Whisk the flour, baking powder, baking soda, pumpkin pie spice, cinnamon, and salt together in a large mixing bowl.
In a separate bowl, stir together the pumpkin puree, sugar, brown sugar, oil, and vanilla.
Add the pumpkin mixture to the bowl with the flour mixture, then stir just until combined. Don't overmix — a few lumps are fine. The batter will be very thick and fluffy.
Drop the batter by 2 tablespoon rounds (a cookie scoop works great here) on the prepared baking sheets, spacing them at least 3 inches apart. You can bake the cakes in 2 batches if you don't get through all the batter on the first one.
Bake the cakes until they've spread out and puffed up, and the tops feel set, about 14 to 16 minutes. Lightly touch the top of one with your finger to test for doneness; it should spring back.
Place the baking sheets on cooling racks and let the cakes cool for about 5 minutes, then remove them from the sheets and transfer them directly to the racks to finish cooling.
Make the filling while the cakes cool. First, beat the vegan cream cheese, butter, vanilla, and salt together at high speed with an electric mixer. Begin beating in the powdered sugar at low speed, adding about a cup at a time, until the mixture is thick enough for stuffing the cakes.
Once the cakes are cool, spread or pipe about 2 tablespoons of the filling onto the flat sides of half the cakes, then close each whoopie pie with a second cake to create a sandwich.
Serve immediately or chill in an airtight container in the fridge for up to 3 days.