Preheat oven to 350 degrees. Line baking sheet with parchment paper or use baking stone.
Add the rolled oats to a food blender and pulse several times until oats are slightly shopped up. Pour oats into a large bowl and add the flour, baking powder, baking soda, cinnamon, and salt. Whisk until ingredients are combined. Set aside.
In the bowl of a stand mixer, beat the butter and sugar on medium-high until light and fluffy, about 3 minutes. Add eggs and vanilla extract and beat for 3 more minutes, scraping down sides of bowl as needed.
With mixer on low speed, gradually add in dry ingredients until just combined.
Using a cookie scoop, drop level scoops of dough onto prepared cookie sheet. Bake for 10-12 minutes or until edges just begin to brown. Set tray on cooling rack for about 5 minutes before transferring cookies to cooling rack to cool completely.
When cookies are completely cool, combine the cream, water, and molasses in a small bowl. Stir or whisk until the molasses is incorporated. Add the powdered sugar and stir until sugar is completely incorporated and mixture is thickened.
With a spoon, spread icing on top of cooled cookies, smoothing until completely covered. Icing will set after an hour, then store cookies in airtight container.