Preheat the oven to 350 degrees. Place the oats in a food processor and pulse about a dozen times. Be careful not to grind them into flour, you want a variety of oat textures. Pour the oats into a mixing bowl and add the flours, starches, baking powder, soda, salt, cinnamon, and nutmeg. Stir to combine.

In a separate mixing bowl, beat the butter on medium speed for about 30 seconds. Add the sugars and continue beating until the batter is light and fluffy, about 2 minutes. Add the eggs and vanilla, beat again until combined. Add about 1/2 of the dry ingredients and mix on low speed to combine. Add the remaining ingredients and mix again until combined.

Scoop generous cookie dough mounds (about 2 tablespoons worth) onto a parchment lined baking sheet. (Plan for 6 cookies on a tray, they will spread a good bit.) Bake for 10-12 minutes, just until the bottoms of the cookies begin to brown. Do not overbake.

Remove from the oven and allow the cookies to cool on the tray for at least 5 minutes before transferring them to a wire rack to cool completely. Place the powdered sugar in a bowl and slowly stir in 3 tablespoons of milk. Add an additional tablespoon slowly, stirring until the icing is thin enough to drizzle. Add only enough milk to achieve the correct consistency. Drizzle the icing over the cool cookies. Let dry before storing. Cookies can be kept in an airtight container in the refrigerator or with the lid slightly cracked at room temperature for a crispier cookie. Enjoy!