Preheat oven to 350 degrees F. In a large bowl, beat 2 cups butter with an electric mixer on medium speed until light and fluffy. Add granulated sugar, baking powder, baking soda, salt, cinnamon, and nutmeg. Beat until combined, scraping bowl occasionally. Add eggs and 2 teaspoons vanilla; beat until combined. Beat in pumpkin. Add the flour slowly until combined. Dough will be very wet.
Drop dough by the tablespoon onto parchment lined sheets. Bake in the preheated oven for 10 to 12 minutes or until tops are set. Transfer cookies to a wire rack; let cool.
For the frosting: Beat all of the ingredients until soft and whipped. Frost cooled cookies and sprinkle with cinnamon.