Preheat oven to 350 degrees Fahrenheit. Prepare baking sheets with parchment paper, silicone baking mats, or cooking spray.
Place oats in a food processor or blender and pulse 3-5 times. Just enough to break up the oats for a variety of textures, but not so much it turns into ground oat flour.
In a large bowl combine the oats, flour, baking powder, baking soda, salt, cinnamon, and nutmeg. Stir and set aside.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and sugars. Add the eggs and vanilla. Mix well. Scrape bowl. Add the dry ingredients and mix until incorporated.
Scoop cookie dough balls (about 2 Tbsp each) onto prepared baking sheets 3-inches apart (about 6-8 per tray depending on the size).
Bake at 350 degrees Fahrenheit for 9 to 10 minutes or until the bottoms and edges are just starting to brown. Remove cookies from oven and allow to rest for a few minutes. Then transfer to a cooling rack. Cool completely.
Prepare icing by whisking the powdered sugar and vanilla/almond extract in a bowl, while gradually adding the milk/heavy cream to a desired texture. You want it thick, but pourable.
Quickly drop the tops of the cooled cookies into the icing and IMMEDIATELY lift them straight back up. Allow excess icing to drip off, and place the cookies back onto the cooling rack until icing sets. You want to do this fast so you have the cracks peaking through the icing. Store in an airtight container at room temperature.