Using a hand or stand mixer, cream together the butter and sugar until soft and fully.
Turn the speed to low, and beat in the pumpkin puree, egg, and vanilla extract.
In another bowl, combine the dry ingredients: flour, baking powder, spices, and salt.
Mix the dry ingredients into the wet, in a few additions. Beat after each addition, scraping the bottom and sides of the bowl.
Refrigerate the cookie dough for at least 30 mins
In a small bowl, combine the sugar and cinnamon (for rolling the cookies)
Make balls of about 2 tbsp of cold cookie dough and roll them into the cinnamon sugar.
Place the cookie balls on two baking sheets lined with parchment paper. Make sure to leave some space between them. Lightly press them down with the bottom of a glass and bake for 10-12 mins or until the edges are slightly brown. Let them cool down on the baking sheet for 5 minutes and transfer to a cooking rack.
Make the frosting: combine all the frosting ingredients in a bowl and beat until smooth.
Top each cookie with about a tsp of frosting and sprinkle additional cinnamon on top.