Pulse the oats 10 times in a food processor. Don’t over-pulse, we don’t want them too powdery or the cookies won’t have the right texture.
Add the butter, brown sugar, egg, and vanilla to a large bowl and whisk to combine.
Add the pulsed oats, flour, cinnamon, salt, baking soda, baking powder, and nutmeg to the butter mixture. Stir to combine. The dough will be wet at this point.
Cover the bowl with plastic wrap, and chill for 15 minutes in the freezer. The dough will have stiffened up perfectly after chilling 15 minutes in the freezer.
Preheat the oven to 350F. Line 2 large baking trays with silpat liners or parchment paper.
Use a 1-tablespoon scoop to measure out the dough and scoop it onto the prepared baking trays, leaving a couple inches between each dough ball.
Bake the cookies until they’re golden and set along the outside, but still look a touch doughy in the center, about 10 to 12 minutes, rotating the trays once halfway through.
Let the cookies cool for 10 minutes on the trays, and then use a thin metal spatula to transfer them to a wire rack to finish cooling. Bake the remaining cookie dough the same way.
For the Icing:
Stir together all ingredients in a bowl, adding more milk if needed to reach the right consistency.
To Glaze the Cookies:
Lightly dip each cooled cookie into the icing. I like to just barely dip the cookie tops, so that they get a crackled look.
Place the glazed cookies onto a wire rack and let the icing set before serving.
Notes
Storage: Store these cookies in an airtight container at room temperature for up to 1 week. Or you can layer the cookies between pieces of parchment paper in an airtight container and freeze them for up to 3 months.