Preheat the oven to 350°F and line baking sheets with parchment paper.
Whisk together flour, baking powder, baking soda, salt, and spices in a bowl.
In a separate bowl, cream the butter and sugars until light and fluffy.
Beat in the egg, pumpkin puree, and vanilla until smooth.
Gradually add the dry ingredients and mix until just combined.
Scoop dough onto baking sheets, spacing 2 inches apart.
Bake 11–13 minutes or until set and lightly golden.
Let cool completely on a wire rack before frosting.
To make the frosting, beat butter, powdered sugar, cinnamon, milk, and vanilla until creamy.
Spread frosting on cooled cookies and let set before serving.
