In a medium mixing bowl, combine the flour, 1/3 cup cocoa powder, baking soda, baking powder, cinnamon, cloves, and salt until well blended.
In a large mixing bowl, use an electric mixer to beat the butter with the brown sugar and granulated sugar until well-blended. Beat in the pumpkin puree, egg, and 1 teaspoon of vanilla extract until completely blended. Gradually beat in the flour mixture.
Drop the batter by heaping tablespoons on a baking sheet with at least 2 inches between each cookie. Bake for about 16 minutes until the edges are firm and the middle isn’t mushy. Cool on the baking sheets for two minutes, then transfer the cookies with a spatula to a wire rack to cool completely.
Make the Icing:
While the cookies are baking and cooling, make the frosting. In a medium mixing bowl, use a mixer to blend together the confectioners’ sugar, 1/4 cup cocoa powder, milk, 1 tablespoon melted butter, 1 teaspoon vanilla extract, and a pinch of salt until smooth.
When the cookies have cooled completely, spread the frosting over the cookies. Let the frosting set for about 30 minutes at room temperature.
Notes
Leave at least 2 inches between each cookie when baking.
Bake until the edges of the cookies are firm and the middle isn’t mushy.
While the cookies are baking and cooling, make the frosting.
These will keep at room temperature in a sealed container for about 4 days.