In a medium bowl, whisk together the flour, baking soda, cinnamon, nutmeg, cloves, and salt. Set aside.

In a large bowl (or stand mixer), cream together the softened butter and granulated sugar until light and fluffy (3-5 minutes).

Beat in the pumpkin puree until well combined. Add the egg and vanilla extract and mix until smooth. Scrape down the sides of the bowl.

Gradually add the dry ingredients to the wet ingredients, mixing on low speed until just combined. Do not overmix.

Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 1 hour (up to 24 hours).

Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or silicone baking mats.

Use a cookie scoop or spoon to drop rounded tablespoons of dough onto the prepared baking sheets, leaving about 2 inches between each cookie.

Bake for 10-12 minutes, or until the edges are lightly golden brown and the centers are set.

Remove the baking sheets from the oven and let the cookies cool on the baking sheets for a few minutes before transferring them to a wire rack to cool completely.

In a large bowl (or stand mixer), cream together the softened cream cheese and butter until smooth and creamy.

Gradually add the powdered sugar, one cup at a time, beating on low speed until combined.

Beat in the vanilla extract. Then, add milk (or heavy cream) one tablespoon at a time, until the frosting reaches your desired consistency.

Once the cookies are completely cool, frost them with the cream cheese frosting.

Serve the frosted cookies immediately, or store them in an airtight container in the refrigerator for up to 3 days.