Preheat the oven to 350° F. In a large mixing bowl, combine the flour, baking powder, baking soda, cinnamon, nutmeg, ground cloves, and salt; set aside.
In a medium sized bowl using a hand mixer, mix the butter and sugar for 3 minutes, or until creamy. Add the pumpkin, egg, and vanilla to the butter mixture and mix for 2 minutes or until creamy. Stir in dry ingredients.
Drop 1 tablespoon of cookie dough on the baking sheet and flatten slightly. *tip: I flattened by using the back of a tablespoon that I had dipped slightly in water to prevent sticking.
Bake for 15 minutes in the preheated oven or until cookies have puffed and are no longer wet on top. Cool the cookies completely.
FOR THE ICING
In a medium sized mixing bowl, combine the confectioners' sugar, milk, melted butter, and rum. Add 1 tablespoon at a time as needed to achieve spreading consistency.
Frost each cookie with the icing and sprinkle with fall colored sprinkles (if desired).