Preheat oven to 375° and Line 3 baking sheets with parchment paper.
In the bowl of a stand mixer, beat butter until smooth and fluffy. Add in sugars and mix on medium low until well blended, scraping down the sides of the bowl with a rubber spatula. Next, add in eggs one at a time, making sure the first egg is mixed in before adding the second one. Then add in vanilla.
With the mixer on low, add in flour, cinnamon, salt, baking soda and powder. Mix for a few seconds just to get dry ingredients incorporated. Add in oats and mix on low, scraping down the sides of the bowl once with a rubber spatula. Finish mixing until ingredients are just combined and there are no white streaks of flour showing.
Scoop a tablespoon sized mound onto your parchment lined pans.
With two fingers, slightly flatten the cookies in the center. Don't completely flatten the cookie, just flatten the centers a little.
Bake for 10-12 min, until the edges are lightly browned and the centers have puffed slightly.
Let cookies cool completely before icing.
To Make The Icing:Combine the confectioners' sugar, whole milk, and vanilla in a small bowl. Stir until very smooth. Spread a thin layer of icing over the top of the cooled cookies and allow excess icing to drip down the sides. Once icing is dry, store cookies in an airtight container.