Make the cookies: Preheat oven to 350 degrees. Line two baking sheets with parchment paper or a nonstick baking mat; set aside.
In a large bowl, whisk together flour, salt, baking powder, baking soda, cinnamon, ginger, and cloves; set aside. In another large bowl, whisk together brown sugar and oil until well combined. Add pumpkin puree and whisk until combined. Add eggs and vanilla and whisk until well combined. Sprinkle flour mixture over pumpkin mixture and whisk until fully incorporated.
Using a tablespoon, scoop dough and level it, then place it on a cookie sheet. Repeat and place about 1 inch apart. Transfer to oven and bake until cookies are just starting to crack on top and a toothpick inserted into the center of each cookie comes out clean, about 15 minutes. Let cool completely on pan.
Make the filling: Sift confectioner' sugar into a medium bowl; set aside. In the bowl of an electric mixer fitted with the paddle attachment, beat butter until smooth. Add cream cheese and beat until well combined. Add confectioners' sugar and vanilla, beat just until smooth. (Filling can be made up to a day in advance. Cover and refrigerate; let stand at room temperature to soften before using.)
Assemble the whoopie pies: Line a baking sheet with parchment paper and set aside. Transfer filling to a disposable pastry bag and snip the end. When cookies have cooled completely, pipe a large dollop of filling on the flat side of half of the cookies. Sandwich with remaining cookies, pressing down slightly so that the filling spreads to the edge of the cookies. Transfer to prepared baking sheet and cover with plastic wrap. Refrigerate cookies at least 30 minutes before serving and up to 3 days.