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

In a large mixing bowl, cream together the softened butter, granulated sugar, and brown sugar until light and fluffy, about 2-3 minutes.

Mix in the pumpkin puree, egg, and vanilla extract until fully combined.

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

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

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

Bake in the preheated oven for 12-14 minutes, or until the cookies are set and the edges are just lightly golden.

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

To make the frosting, beat the softened butter in a medium bowl until smooth. Gradually add the powdered sugar, 1 cup at a time, mixing until combined.

Add the milk, vanilla extract, and ground cinnamon (if using), and continue to beat until the frosting is smooth and creamy.

Once the cookies are completely cooled, spread a generous layer of frosting over each one.

Store the cookies in an airtight container at room temperature for up to 3 days, or refrigerate for longer storage.