With an electric mixer, beat together granulated sugar and vegetable oil.
Add egg, milk, canned pumpkin, and vanilla and blend well.
In a separate bowl, mix together the dry ingredients. Add the dry ingredients to the wet ingredients and mix, just until incorporated.
Drop batter by spoonfuls onto a greased cookie sheet. Bake at 375 degrees F for 10-12 minutes. Allow to cool before frosting.
In a medium saucepan, combine butter, heavy whipping cream, brown sugar, and salt, and cook over medium heat, stirring constantly, until the mixture comes to a boil.
Remove from the heat and stir in vanilla and 1 cup powdered sugar. Let the frosting cool to room temperature and then stir in enough additional powdered sugar to make a good frosting consistency (you may not use the whole extra cup).
Spread the frosting over the cooled cookies.
