Preheat oven to 350 degrees F. Line cookie sheets with parchment paper and set aside.
Place flour, baking powder, baking soda, cinnamon, nutmeg, and salt in the flour sifter. Sift into a large bowl. Set aside.
In a large separate bowl, using an electric mixer on medium speed, cream together the sugar butter. Add pumpkin puree, egg, and vanilla to the butter mixture and mix together well.
Add dry ingredients to wet ingredients and using a wooden spoon, stir until incorporated.Using a tablespoon sized cookie scoop, drop dough ball on prepared cookie sheets.
Bake 14 minutes until edges are golden and top of cookie is no longer wet. Cookie will spring back when lightly touched.
Transfer to a wire rack and cool.
For the frosting:
Melt butter in saucepan over medium heat. Cook just until butter begins to brown.
Add coffee granules, milk, and brown sugar. Bring syrup to a slow boil. Cook for 1 minute.
Remove syrup from heat and let cool completely. When cooled, stir in powdered sugar, vanilla, and heavy cream.
Spoon frosting over cooled cookies and sprinkle with freshly grated nutmeg.
Notes
Adjust the thickness of the icing to your own preference, add more confectioners sugar for a thicker consistency andless powdered sugar for a runnier consistency