In a large bowl, beat the butter until fluffy. Then beat in the sugar, baking powder, baking soda, salt, cinnamon, and nutmeg until well blended.
Add the egg and vanilla and beat to combine. Beat in the pumpkin.
Then, beat in the flour just until combined.
Drop heaping spoonfuls of dough on a cookie sheet. I use a cookie scoop. Bake at 350 degrees for 10-12 minutes until the tops are set.
Transfer to a cooling rack.
For the frosting, add the ingredients in a bowl and blend until smooth and well combined. Spread frosting on cooled cookies. Makes about 3 dozen cookies.