Preheat oven to 350°F. Line baking sheets with parchment paper.
Pulse oats in a food processor 10-12 times. The idea is to break up the oats to create a variety of textures without turning it into ground oat flour.
2 cups old-fashioned oats
In the bowl of a stand mixer, beat butter, brown sugar, and granulated sugar until light, about 2-3 minutes.
1 cup salted butter, 1 cup dark brown sugar, 1/2 cup granulated sugar
Add eggs and vanilla and mix again. Scrape the bottom and sides of the bowl.
2 large eggs, 2 teaspoons vanilla extract
Add the oats, flour, baking powder, baking soda, salt, cinnamon and nutmeg and mix until combined.
2 cups all-purpose flour, 1 Tablespoon baking powder, 1 teaspoon baking soda, 1/2 teaspoon salt, 1 1/2 teaspoons cinnamon, 1/2 teaspoon ground nutmeg
Scoop 1 1/2 to 2 tablespoon-sized balls of dough onto the baking sheet, spacing them 3 inches apart so they can spread.
Bake for 10-12 minutes until the edges are just beginning to brown. The centers will still look soft.
Let the cookies rest for a minute or two before transferring to a wire cooling rack and allowing to cool completely.
Make icing by whisking the powdered sugar, vanilla, and milk in a medium bowl. It should be a thick icing, but still liquid enough to settle when a spoonful of icing is drizzled back into the bowl.
2 cups powdered sugar, 1/4 teaspoon vanilla extract, 2 Tablespoons milk
Give the tops of the cooled cookies a quick dip into the icing and lift them straight up, allowing the excess to drip off. Place the iced cookies back on the wire rack and let the icing set, about 1 hour. Store in an airtight container for up to 1 week.