Preheat the oven to 350°F (175°C). Line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt.
In another large bowl, combine pumpkin, brown sugar, oil, egg, and vanilla extract. Stir until smooth.
Add dry ingredients to the pumpkin mixture and stir until just combined.
Drop spoonfuls of dough onto prepared baking sheets, spacing them about 2 inches apart. Bake for 10 minutes or until the edges are firm. Cool completely on wire racks.
For the filling, beat together cream cheese, butter, powdered sugar, and vanilla extract until smooth and creamy.
To assemble the whoopie pies, spread the filling on the flat side of one pumpkin cookie and top with another cookie.
Notes
Refrigerate assembled whoopie pies for up to 3 days. Serve chilled or at room temperature.