In a medium bowl, whisk together the dry ingredients: flour, baking soda, cinnamon, nutmeg, and cloves.

In a large mixing bowl, cream together butter and sugar until light and fluffy.

Mix in pumpkin puree, egg, and vanilla until well combined.

Gradually add dry ingredients to the wet mixture, mixing until combined.

Cover the bowl and chill the dough in the refrigerator for at least 1 hour.

Preheat the oven to 350°F (175°C) and prepare baking sheets.

Scoop mounds of dough onto prepared sheets, spacing them about 2 inches apart.

Bake for 10-12 minutes until the edges are golden and centers are soft.

Cool on sheets for 5 minutes, then transfer to wire racks to cool completely.

Beat together cream cheese and butter until smooth, then add powdered sugar and milk until desired consistency is reached.

Frost cooled cookies with the cream cheese mixture.

Allow frosted cookies to set for 15 minutes before serving.