Preheat the oven to 350°F and line two baking sheets with parchment paper.
In a large bowl, whisk the pumpkin, brown sugar, granulated sugar, oil, eggs, and vanilla until smooth.
In another bowl, whisk the flour, pumpkin pie spice, cinnamon, baking powder, baking soda, and salt. Fold into the wet ingredients just until combined. The batter will be thick.
Pipe or scoop tablespoon-size mounds about 2 inches apart, keeping them the same size.
Bake 11 to 13 minutes, until the tops spring back. Cool on the pan 5 minutes, then transfer to a rack to cool completely.
Make the Filling and Assemble
Beat the cream cheese and butter until smooth, about 1 minute. Add the vanilla, cinnamon, and salt, then beat in the confectioners' sugar a cup at a time until thick and pipeable.
Match the cooled rounds into pairs by size. Pipe or spread a thick layer of filling on the flat side of one round and top with its match.
Chill the assembled whoopie pies for 20 minutes so the filling sets.
Notes
Keep the batter thick: Thick batter bakes into domes; thin batter spreads flat.
Pipe for even rounds: Uniform rounds sandwich cleanly.
Cool completely: Warm rounds melt the filling.
Storage: Refrigerate filled pies in an airtight container up to 3 to 4 days.