Preheat your oven to 350 degrees.
Line your cookie sheets with parchment paper or lightly spray with non-stick cooking spray. Tip - I like to measure out all my dry ingredients, especially the spices and baking soda/powder and salt, so I can just dump them in when it's time.
In a large bowl, (these can be made with a hand mixer or a stand mixer), cream the softened butter and sugar. Add the egg and vanilla.
Beat in the canned pumpkin.
Add the baking soda, baking powder, salt, cinnamon, nutmeg, and cloves.
Mix in the flour at a medium speed to make a sticky dough.
You might be tempted to add more flour, but don't, or you will end up with dry cookies.
Scoop the cookie dough onto the prepared baking sheet using a #40 cookie scoop or by the tablespoonful. Bake for 12 minutes at 350 degrees.
Cool on the baking sheet slightly before transferring to a wire rack to cool completely before frosting with cream cheese frosting. Store these cookies in the fridge between layers of wax paper.
To make the cream cheese frosting, cream the softened cream cheese and softened butter in a medium bowl.
Beat in the vanilla and powdered sugar.
Beat until completely smooth.
Frost completely cooled cookies. If they're still warm, the frosting will melt off the tops.