Prep the equipment: Preheat the oven to 350 F. Line two large baking sheets with parchment paper and set aside.
Mix dry ingredients: In a large bowl mix together all-purpose flour, old-fashioned oats, baking soda, cinnamon and kosher salt.
Cream wet ingredients: In a separate large bowl fitted with a hand or stand mixer, beat together butter, white sugar, and brown sugar until light and fluffy. Add in pumpkin puree, vanilla extract, and egg to the butter mixture until combined.
Mix cookie batter: Slowly add the dry mixture to the wet mixture and beat together until just combined.
Form cookies: Drop ¼ cup dough balls onto the baking sheet spread out apart from each other.
Bake and cool: Bake for 10-12 minutes or until the sides are golden brown. Cool on a cooking rack for 5-10 minutes to cool completely before frosting.
Make frosting: In a medium bowl fitted with a stand or hand mixer add in cream cheese, maple syrup, powdered sugar, pumpkin pie spice and a pinch of kosher salt. Mix together until mixture is creamy and smooth, but still spreadable. Add in 1-2 tsp of milk or half and half if the mixture is too thick.