Cream together butter and sugars with electric mixer and paddle attachment.
Add pumpkin, egg, vanilla, and corn syrup. Beat well for 1 minute.
In a separate mixing bowl, combine flour, baking soda, baking powder, spices, and salt. Add dry ingredients to wet slowly, and mix just until combined.
Dough will be very sticky.
Use a tablespoon measure to drop 1 tablespoon of dough on cookie sheet. Wet the back of a spoon and use it to flatten the dough down.
Bake for 12-13 minutes or until bottoms look slightly golden. Don't overbake or cookies may become dry.
For the Frosting:
Cream butter in an electric mixer with paddle attachment until light and fluffy.
Add in powdered sugar, 1 cup at a time alternating with heavy cream until desired consistency is reached. Add more powdered sugar if you like a thicker frosting and more heavy cream if you like a looser frosting.
Add in spices and stir to combine.
Pipe frosting on cooled cookies.
Garnish with a dash of cinnamon or pumpkin pie spice! (Optional)