Preheat oven to 350 degrees F. Line baking sheets with parchment paper.
Add oats to a food processor. Pulse just a few times until it becomes a mixture of coarse chopped oats and some oat flour.
1 ¾ cups old fashioned rolled oats
If the food processor bowl is large enough, remove the blade and add the flour, cinnamon, nutmeg, baking powder, baking soda, and salt. Stir to combine. (If the food processor isn’t large enough, you can do this in a mixing bowl instead)
1 cup all purpose flour, 1 ½ teaspoons ground cinnamon, ¼ teaspoon ground nutmeg, ½ teaspoon baking powder, ½ teaspoon baking soda, ¼ teaspoon kosher salt
In the bowl of a stand mixer fitted with the paddle attachment, add butter, brown sugar, and granulated sugar. Beat until light and creamy, about 3 minutes on medium speed.
½ cup salted butter, 1 cup light brown sugar, ¼ cup granulated sugar
Beat in the egg and vanilla until combined, scraping down the bowl as needed.
1 large egg, 1 teaspoon vanilla extract
Add the dry ingredients. Mix until just incorporated.
Drop 1 ½ tablespoons of cookie dough per cookie, about 2-inches apart, on the prepared baking sheets.
Bake for 10-15 minutes, or until golden brown. Allow to cool on the cookie sheet.
Once cooled, prepare the icing by adding sifted powdered sugar to a medium bowl.
1 ½ cups sifted powdered sugar
Add the vanilla and 1 ½ tablespoons milk. Whisk to combine. It should be thick, if you need more milk, add it slowly.
¼ teaspoon vanilla extract, 1 ½ to 2 tablespoons milk
Lightly dip the tops of each cookie into the icing.
Place cookies back on the baking sheet iced side up to allow the icing to set. It may take a few hours to set until they’re stackable.
Notes
Oats: I haven't tried using quick oats in this recipe.
Butter: If using unsalted butter, increase the salt to 1/2 teaspoon.
Salt: If you don't have kosher salt or sea salt, use half the amount of table salt.
Vanilla: If you want to glaze to be as white as possible, use clear vanilla.