How to Make It
Make the cookies: Heat oven to 350° F with the racks in the upper and lower thirds. Line 2 large rimmed baking sheets with parchment. In a medium bowl, whisk together the flour, pumpkin pie spice, baking powder, baking soda, and salt; set aside.
In a large bowl, whisk together the pumpkin puree, sugars, oil, egg, and vanilla until combined. Mix in the flour mixture until just moistened (do not overmix).
Drop mounds of the dough (about 2 tablespoons each) onto the baking sheets, spacing them 2 inches apart. Bake until golden and firm to the touch, 12 to 14 minutes. Let cool for 5 minutes in the pan, then transfer to a wire rack to cool completely.
Make the filling: With an electric mixer, beat the cream cheese, butter, confectioners’ sugar, and vanilla until fluffy, 2 to 3 minutes.
Make the whoopie pies: Spread a heaping tablespoon of filling on the flat side of half the cookies. Top with the remaining cookies. If soft, chill for 20 to 25 minutes.
Storage suggestion: Keep the whoopie pies refrigerated, between sheets of wax paper in an airtight container, for up to 1 day. Bring to room temperature before serving, if desired.