Preheat oven to 350. Line a cookie sheet with parchment.
Cream shortening, sugar, egg, pumpkin and vanilla.
Add all the dry ingredients and stir until combined.
Scoop small spoonfuls (about 1 tablespoon) of batter onto the cookie sheet, spacing about 2" apart. Bake for 10-11 minutes in the 350 degree oven.
While baking, combine all the frosting ingredients in a small bowl, whisking or beating with a mixer to combine.
Let the cookies cool completely, and then frost. Enjoy! We love these stored in the fridge or freezer for a thicker frosting texture.
Cookies can be frozen in a single layer and then stored in the freezer in a sealed container for 3+ months.