Preheat oven to 350 degrees. Line baking sheets with parchment paper.
In a food processor add oats and pulse for 10 seconds to roughly break the oats up.
In a large bowl, whisk together, oats, flour, cornstarch, baking powder, baking soda, salt, cinnamon, and nutmeg.
In the bowl of a stand mixer or a large bowl if mixing by hand, cream together butter, brown sugar, white sugar and vanilla until light and fluffy about 2 minutes.
Add egg and mix slowly to combine.
Add the dry ingredients slowly until combined.
You can work with the dough now, or refrigerate the dough for 30 minutes if its too soft.
Scoop dough out with a 1 inch cookie scoop and place onto prepared baking sheets. (If you want a more soft cookie center, leave dough in rounded shape on pan. If you want a more flat cookie, flatten dough with a piece of parchment paper and the bottom of a glass.)
Place in oven and bake between 10-14 minutes until cookie gets a nice golden tinge to edge of cookie. For a more crisp cookie leave in for the 14 minutes. Remove from oven and allow to rest for a few minutes, then take cookies off of baking sheet and place on wire rack to completely cool.
After the cookies are cooled, whisk together in a small bowl, powdered sugar, milk, and vanilla. Add more milk if needed for a smooth icing or add more powdered sugar to thicken icing up.
Take a cookie and hold upside down and dip into icing. Twirl to remove excess icing and place back onto wire rack to set icing for 30 minutes. Enjoy.