Preheat your oven to 350°F (175°C). Line baking sheets with parchment paper or lightly grease them.

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy.

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

In a separate bowl, whisk together the all-purpose flour, baking powder, baking soda, cinnamon, nutmeg, cloves, and salt.

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

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

Bake in the preheated oven for 10-12 minutes, or until the edges are lightly golden and the cookies are set.

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

To make the frosting, whisk together the powdered sugar, heavy cream, and vanilla extract in a bowl until smooth and spreadable.

Once the cookies are completely cooled, spread a thin layer of frosting over each cookie using a butter knife or offset spatula.

Allow the frosting to set before serving. Store leftovers in an airtight container at room temperature or in the refrigerator.