Begin by gathering all the necessary ingredients. Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius) and lightly grease two baking sheets.

In a medium mixing bowl, combine the all-purpose flour, ground cinnamon, baking powder, baking soda, ground nutmeg, ground cloves, and salt.

In a separate mixing bowl, cream together the softened butter and white sugar until the mixture is light and fluffy, approximately 2 to 3 minutes. Incorporate the pumpkin puree, egg, and vanilla extract, mixing until the blend is creamy. Gradually add the flour mixture, stirring until fully combined.

Using a tablespoon, drop portions of the dough onto the prepared baking sheets, gently flattening each scoop.

Bake in the preheated oven for 15 to 20 minutes, or until the centers are set, switching the baking sheets halfway through for even baking. Once done, transfer the cookies to a wire rack and allow them to cool to room temperature, which should take about 30 minutes.

While the cookies cool, prepare the icing by mixing the confectioners' sugar, milk, melted butter, and vanilla extract in a bowl until the mixture is smooth. Adjust the consistency by adding more milk if necessary, until it is suitable for drizzling.

Once the cookies have cooled, use a fork to drizzle the icing over the top of each cookie, creating a delightful finish.