Preheat oven to 350 degrees F. Prepare 2 baking sheets lined with parchment paper or a Silpat mat.
Add the rolled oats to a food processor and pulse 10 times. Don't over process because you want a variety of textures not just a ground oat flour. In a large mixing bowl combine the oats, flour, baking powder, soda, salt, cinnamon and nutmeg. Whisk or stir to combine. Set aside.
In the bowl of a stand mixer beat the butter on medium-high about 30 seconds. Add the brown and granulated sugars and mix on medium-high until the batter lightens and becomes fluffy. Add the eggs, one at a time, beating just until the yolk disappears into the batter. Lightly beat in the vanilla. Add about ⅓ of the oat and flour mixture to the butter and egg mixture, mixing on a low speed just until blended. Continue adding the flour mixture until it is fully incorporated.
Using a 2 tablespoon size ice cream or cookie scoop (not heaping - leveled straight across the top of the scoop), roll the dough into balls and place on the prepared baking sheet at least 2-inches apart. I was able to fit 6 cookies at a time on each pan. Bake for 10-12 minutes or until the bottoms just being to brown. Do not over bake.
Remove the pan from the oven and let the cookies rest for 5 minutes before removing to a rack to cool completely.
To prepare the icing combine the confectioners' sugar with the milk or cream and/or water. Whisk until the sugar is dissolved and the icing is somewhat thick. Place the icing in a shallow dish or container, about 4x4 inches. Quickly dip the tops of the cooled cookies into the icing and let the excess drip off. Set the dipped cookie on the rack until the icing has set.
Store the cookies in an airtight container or refrigerator. I stored mine in the fridge and they were perfect!