Preheat the oven to 350°F and line two baking sheets with parchment paper.
Mix the sugar, brown sugar, and oil in the bowl of a stand mixer until fully combined.
Add the pumpkin puree, eggs, and vanilla, mixing again until smooth and evenly blended.
Combine the flour, salt, baking soda, baking powder, and pumpkin pie spice in a separate bowl. Gradually add the dry mixture to the wet ingredients, mixing just until combined. Scrape down the sides to make sure everything is incorporated, but don’t overmix.
Scoop the batter using an ice cream scoop, placing even mounds on the prepared baking sheets with a little space between each for spreading.
Bake for 10 to 12 minutes, or until the centers are set. Let them cool completely on the parchment before removing.
Beat the softened butter in a stand mixer until smooth. Add the cream cheese and continue mixing until lump-free.
Add the powdered sugar and vanilla, then mix until fully combined. Increase the speed to medium and whip until the frosting is smooth and fluffy, scraping down the sides as needed. Transfer to a piping bag.
Pair up the cooled cookies with ones of similar size. Pipe a mound of frosting onto the flat side of one cookie, then top with its pair to form a sandwich.