In a mixing bowl whisk together the flour, baking powder, baking soda, cinnamon, nutmeg, and salt.
In the bowl of a stand mixer fitted with the paddle attachment, beat the butter, brown sugar, and granulated sugar on high until light and fluffy, about 3-4 minutes.
Beat in the eggs and vanilla extract; scraping down the sides of the bowl as needed.
Add the flour mixture to the butter mixture in 2-3 smaller additions, mixing well after each addition.
Stir in the rolled oats, then cover and refrigerate for 30 minutes.
Preheat the oven to 350°F/180°C or 160°F fan oven, and line 2 baking sheets with parchment paper or Silpat silicone mats.
Using a medium cookie scoop (# 40 or 1 ½ inch), drop the dough onto the prepared baking sheets 2” apart, press down slightly to flatten.
Bake in the preheated oven for 8-10 minutes, or until lightly golden and no longer glossy on top.
Remove from the oven and allow to cool 5 minutes before transferring to a cooling rack and cooling completely.
Stir together the powdered sugar and milk until it becomes a thick, smooth icing.
Quickly tap the tops of the cookies on the surface of the icing and allow the excess to drip off.
Allow the icing 20 minutes to set before stacking.
Notes
Let the Cookies Cool! If you add icing to oatmeal cookies that are still warm, the icing will melt and soak in and you won't be able to see it.
Drizzle or Dip: I love the way these cookies look with the icing covering the tops and settling into the little nooks and crannies, but you can also drizzle the icing over the cookies with a spoon if you prefer.
To Store: Be sure to let the icing dry completely before stacking or storing. Store oatmeal cookies in an airtight container. They'll stay fresh at room temperature for about a week, or in the fridge for up to two weeks.
To Freeze: If you'd like to freeze these cookies, flash freeze them first in a single layer for about an hour. Then you can transfer them to a freezer bag or container and store for up to 3 months.
To Freeze the Dough: Freeze unbaked cookie dough, scooped into balls. Flash-freeze the dough balls, then transfer them to a ziptop bag for storage. Bake the frozen dough directly from the freezer, just add 2-3 minutes to the baking time.