Preheat oven to 350 degrees F. Combine flour, baking powder, baking soda, cinnamon, nutmeg, ground cloves, and salt; set aside.
In a medium bowl, cream together the ½ cup of butter and white sugar. Add pumpkin, egg, and 1 teaspoon vanilla to butter mixture, and beat until creamy. Stir in dry ingredients.
Drop on cookie sheet by tablespoonfuls; flatten slightly. Bake for 15 to 20 minutes in the preheated oven. Cool cookies completely.
For the icing
Combine confectioners' sugar, milk, melted butter, and rum extract. Add milk as needed, to achieve drizzling consistency.