Preheat oven to 350 degrees. Line two baking sheets with parchment paper.
Place the oats in a blender and pulse for about 10 seconds or until the oats are coarse. They should still have some texture.
In a bowl, stir together the oats, flour, baking powder, soda, salt, cinnamon, and nutmeg.
In the bowl of an electric mixer, cream together the butter and sugars. Add in the eggs, one at a time, beating well after each addition. Beat in the vanilla.
Slowly add the oat mixture to the butter mixture and beat until well combined.
Scoop the cookies out onto the prepared baking sheets using a standard cookie scoop (about 1½ Tablespoon balls), spacing them at least 1.5 inches apart. Bake for 10-12 minutes or until bottoms begin to brown. For soft, chewy cookies, pull them out when the centers are still soft. For crisper cookies, continue to let them bake until centers are set. Allow the cookies to set up on a baking sheet for 5 minutes before transferring to a cooling rack.
Meanwhile, whisk together the powdered sugar and milk until smooth. When the cookies are cooled, spread the frosting on top. Feel free to color the frosting or sprinkle with holiday themed sprinkles if desired!