Preheat the oven to 350 degrees F. Line two baking sheets with parchment paper.
In a large bowl, whisk the flour, salt, baking powder, baking soda, cinnamon, ginger, and cloves together and set aside.
In a separate bowl, whisk the brown sugar and oil together until combined. Add the pumpkin puree and whisk to combine thoroughly. Add the eggs and vanilla and whisk until combined.
Sprinkle the flour mixture over the pumpkin mixture and whisk until completely combined.
Use a small ice cream scoop with a release mechanism to drop heaping tablespoons of the dough onto the prepared baking sheets, about 1 inch apart. Bake for 10 to 12 minutes, until the cookies are just starting to crack on top and a toothpick inserted into the center of a cookie comes out clean. Remove from the oven and let the cookies cool completely on the pan while you make the filling.
Sift the confectioners' sugar into a medium bowl and set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat the butter until it is completely smooth, with no visible lumps. Add the cream cheese and beat until combined.
Add the confectioners' sugar and vanilla and beat until smooth. Be careful not to overbeat the filling, or it will lose structure. (The filling can be made 1 day ahead. Cover the bowl tightly and put it in the refrigerator. Let the filling soften at room temperature before using.).
Turn half of the cooled cookies upside down (flat side facing up.).
Use an ice cream scoop or a tablespoon to drop a large dollop of filling onto the flat side of the cookie. Place another cookie, flat side down, on top of the filling. Press down slightly so that the filling spreads to the edges of the cookie. Repeat until all the cookies are used. Put the whoopie pies in the refrigerator for about 30 minutes to firm up before serving.
The whoopie pies will keep for up to 3 days, on a parchment-lined baking sheet covered with plastic wrap, in the refrigerator.