Preheat oven to 350°F. Line two to three baking sheets with parchment paper or a slipat. Set aside.
In a large bowl, add flour, sea salt, baking powder, baking soda, cinnamon, ground ginger and ground clove, whisking to combine. Set aside.
In another large bowl, whisk together dark brown sugar and vegetable oil until well combined. Add chilled pumpkin puree, whisking again until combined. Add eggs and vanilla then whisk until well combined. Sprinkle dry mixture (flour and spices) over the wet mixture (pumpkin and oil). Whisk until fully incorporated.
Using an ice cream scoop, drop 1 - 2 tablespoons of dough onto the prepared baking sheets (about 1 inch apart, the cookies will spread a bit). One at a time, transfer the baking sheets to the oven and bake until cookies are just starting to crack on the top. You can also use a toothpick to test doneness. Insert a toothpick into the center of the largest cookie on the sheet. If it comes out clean, the cookies are done (12 - 14 minutes). Let the cookies cool completely on the pan.
While the cookies are cooling, prepare the frosting. Sift confectioners' sugar into a medium sized bowl. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter until very smooth. Add cream cheese and beat until well combined. Add vanilla and mix for a few seconds. Add confectioners' sugar and beat just until smooth (be careful not to overmix the frosting).
To assemble, start by lining a baking sheet or serving platter with parchment paper. (the cake is very moist and can stick to regular surfaces). When the cookies have completely cooled, place half of them cut side up on the prepared baking sheet. One at a time, spoon a heaping tablespoon of frosting on the flat side of a cookie (the measurements above make a lot of frosting, so you can be generous here). Sandwich another cookie on top of the frosting, pressing down slightly to spread the filling to the edges. Repeat with remaining cookies and frosting. Cover finished whoopie pies with plastic wrap and chill in the refrigerator at least 30 minutes before serving.