Preheat oven to 350°F / 180°C / Gas Mark 4
In a medium mixing bowl, combine flour, baking powder, baking soda, salt, cinnamon and nutmeg. Whisk to combine and set aside.
In a separate medium mixing bowl, beat butter and sugar with an electric mixer on medium speed for 2 - 3 minutes until light and fluffy.
Add egg, vanilla and pumpkin. Beat for an additional 2 minutes. (don't worry if it looks curdled, it's fine)
Add flour mixture to pumpkin mixture and beat until combined, but do not over-mix.
Using a small cookie scoop (1 1/2 tbsp.) drop dough 2 inches apart onto lined cookie sheets.
Bake for 12 minutes or until tops are set. Transfer to wire rack to cool completely.
While cookies are cooling, make frosting: With electric mixer, beat all ingredients together until light and fluffy.
Spread frosting on cooled cookies and top with sprinkles, if desired.