Preheat your oven to 350°F (175°C) and line two baking sheets with parchment paper.
In a large mixing bowl, combine the softened butter, brown sugar, and granulated sugar. Use an electric mixer to cream them together until light and fluffy, about 2-3 minutes.
Add the egg, egg yolk, and vanilla extract to the bowl. Beat until fully combined and smooth.
Lightly pulse the oats in a food processor about 10 times. You want them to have a bit of texture, so avoid grinding them too finely. Set them aside.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Avoid overmixing (oats, flour, cinnamon, cornstarch, baking soda, baking powder, and salt.)
If you want to minimize spreading, refrigerate the dough for at least 30 minutes. If you don’t mind the cookies spreading a bit, you can skip this step.
Scoop about 1.5 tablespoons of dough and roll into balls. Place them on the prepared baking sheets, spacing them about 2 inches apart.
Bake the cookies for 10-11 minutes, or until the edges are just set and the centers look slightly underbaked. Remember, the cookies will continue to cook on the hot baking sheet as they cool.
Immediately after removing the cookies from the oven, use a large glass or round cookie cutter to gently shape them into perfect circles while they’re still soft.
Let the cookies cool on the baking sheet for 5 minutes, then transfer them to a wire rack to cool completely.
While the cookies are cooling, whisk together the powdered sugar, milk, and a splash of vanilla extract in a small bowl until smooth. If the icing is too thick, add a little more milk (1 teaspoon at a time) until you get your desired drizzling consistency.
Dip the top of your cookies lightly in the icing.
