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 soda, baking powder, cinnamon, nutmeg, ginger, cloves, and salt.
In a large bowl, use an electric mixer to cream together the butter and both sugars until light and fluffy, about 2-3 minutes.
Add the pumpkin puree, egg, and vanilla to the butter mixture and beat until well combined. Gradually add the dry ingredients, mixing on low speed just until incorporated.
Cover the dough and refrigerate for at least 30 minutes.
Using a cookie scoop or tablespoon, drop rounded portions of dough onto the prepared baking sheets, spacing them about 2 inches apart.
Bake for 12-14 minutes, until the edges are set but the centers still appear soft. Allow 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. Gradually add the powdered sugar, then mix in the vanilla and salt. Beat on medium-high speed for 2-3 minutes until light and creamy.
Once cookies are completely cool, match them in pairs of similar size. Pipe or spread about 2 tablespoons of filling onto the flat side of one cookie, then gently press the second cookie on top, flat side down. Slightly twist as you press to secure the filling evenly.