Preheat oven to 350°F. Line rimmed baking sheets with parchment paper. Set aside.

In a food processor, pulse the oats until they are broken down into crumbs, but not so fine that they become flour.

Add the pulsed oats to a medium mixing bowl along with the flour, baking soda, salt, and cinnamon. Whisk to combine and set aside.

In the bowl of a stand mixer fitted with the paddle attachment or in a large mixing bowl with an electric hand mixer, beat the butter and both sugars on medium speed until light and fluffy, about 3-5 minutes, scraping the sides and bottom of the bowl as needed. Add the eggs and vanilla and mix until well combined. Scrape the sides and bottom of the bowl.

With the mixer on low speed, slowly add the dry ingredients, mixing until the dough is just combined. The dough will be thick.

Use a 1- or 2-tablespoon cookie scoop to portion the dough. Roll each portion into a ball, then place 2 inches apart on the prepared baking sheets. Using the bottom of a jar or glass dipped in water, gently flatten each dough ball slightly.

Bake in the preheated oven for 11-15 minutes (depending on size), or until the tops are no longer shiny and the edges are golden brown. Allow to cool on the baking sheets for 3-5 minutes before transferring to a wire rack to finish cooling.

Once the cookies have completely cooled, whisk the powdered sugar, melted butter, vanilla, and 2 tablespoons of the milk or cream in a medium bowl until smooth. If needed, add the additional ½ tablespoon of milk to reach the desired consistency; you should be able to dip the tops of the cookies into the icing. (If using whole milk you’ll need less than if using heavy cream; if using heavy cream you may need up to 4 tablespoons).

Briefly dip the top of each cookie into the icing. Let the icing set before serving.

Store in an airtight container for up to 4 days or freeze for up to 3 months.