Cream the 1 cup of butter. Then add the sugar and mix until combined and creamy. Add the egg and beat until combined. Add the pumpkin and vanilla. Beat until combined and the pumpkin is thoroughly mixed in. Add the dry ingredients and mix until all ingredients incorporated. Using a spoon, drop cookie dough onto cookie sheet (about 1 to 1.5"). Bake at 350 degrees for 15 minutes or until bottoms of cookies are slightly brown. Place on cooling rack. Allow to cool before you frost.
Combine all ingredients until you have a smooth texture. Using the back of a small spoon, frost each cookie and then sprinkle with Stella's Table Citrus Sea Salt.
This recipe should make approximately 24 cookies.