1. Using a food processor, process rolled oats 5 times. You want the oats to break down a little, but not completely or they will turn into oat flour. A quick burst will do it, press the button five times for one second. Set aside.
2. In a large mixing bowl, or stand mixer with paddle attachment, beat butter, granulated sugar, and brown sugar until light and fluffy.
3. Add in eggs and vanilla and beat until well combined.
4. In a small bowl, combine all-purpose flour, baking powder, baking soda, cinnamon and salt.
5. Gradually add in flour mixture and mix on low speed just until combined.
6. Add in oatmeal and blend on low speed just until combined. The mixture will be thick. Use a spatula to scrape down the sides and mix again once or twice by hand.
7. Using a heaping tablespoon, shape and roll into balls, press down to flatten slightly, then place on ungreased cookie sheet.
8. Bake in 350F oven for 10 to 12 minutes. Cookies will still be soft in the middle.
9. Cool on baking sheet for two minutes, then transfer to wire cooling rack. (cookies must be cooled completely before icing) At least one hour.
10. In a small mixing bowl, combine powdered sugar and milk. If mixture is still thick, add milk, one teaspoon at a time until the consistency is a little runny.
11. Take cooled cookies one at a time and dip the top of the cookie into the icing. Tilt the cookie from side to side and top to bottom to even out the icing. Hold upside down until the excess icing has dripped back into the bowl. Set on wire rack. (clean up will be easier if you place a piece of plastic wrap or paper towelling underneath the wire rack).
If you have little bubbles in the icing, use the tip of a sharp knife to gently pop them and they will disappear.
Allow the icing to set completely before stacking into a plastic storage container.