Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.

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

In a large mixing bowl, use a hand or stand mixer to cream together the softened butter and granulated sugar until light and fluffy, about 2-3 minutes.

Add the pumpkin puree, egg, and vanilla extract to the butter mixture, and mix until well combined.

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

Using a spoon or cookie scoop, drop rounded tablespoons of dough onto the prepared baking sheets, spacing them about 2 inches apart.

Bake the cookies in the preheated oven for 12-15 minutes, or until the edges are set and the tops no longer look wet.

Remove the cookies from the oven and let them cool on the baking sheets for 5 minutes before transferring to a wire rack to cool completely.

While the cookies cool, prepare the cream cheese frosting. In a medium bowl, beat the softened cream cheese and butter together until smooth and creamy.

Add the powdered sugar and vanilla extract to the cream cheese mixture, and beat until well combined. If the frosting is too thick, add 1-2 tablespoons of milk, a little at a time, until the desired consistency is reached.

Once the cookies are completely cool, spread or pipe the cream cheese frosting on top of each cookie.

Store the frosted cookies in an airtight container in the refrigerator for up to 5 days. Bring to room temperature before serving.