Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, pumpkin pie spice, and salt until evenly combined.
In a separate large bowl, beat the brown sugar and oil together until smooth. Add the pumpkin puree, eggs, and vanilla extract, mixing until the batter becomes uniform.
Gradually add the dry ingredients to the wet ingredients, mixing on low speed just until combined. Avoid overmixing.
Cover the bowl with plastic wrap and refrigerate for 30 minutes to firm up the batter.
Using a cookie scoop or tablespoon, drop 1½-tablespoon portions of batter onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 12-14 minutes or until the cookies spring back lightly when touched and a toothpick inserted in the center comes out clean.
Allow the cookies to cool on the baking sheets for 5 minutes before transferring to wire racks to cool completely.
While the cookies cool, beat the cream cheese and butter together until smooth and fluffy, about 2-3 minutes.
Gradually add the powdered sugar, cinnamon, vanilla, and salt, continuing to beat until the filling is light and creamy. For an extra-smooth filling, scrape down the sides of the bowl halfway through mixing.
Once the cookies have cooled completely, match them up in pairs of similar size.
Pipe or spread a generous amount of filling (about 2 tablespoons) onto the flat side of one cookie, then gently press the flat side of its matching cookie on top to create a sandwich.