Brown the butter: For a detailed tutorial, see this post on how to brown butter. Set aside & cool slightly for 10-15 minutes. 12 Tbsp. butter, unsalted
Preheat the oven to 375°F. Line 2 cookie sheets with parchment paper or silicone baking mats. Set aside.
Pulse the oats in a food processor about 10 times. They should have some texture to them, not finely ground. Set aside.
1 cup old fashioned oats
Add the sugars to the slightly cooled brown butter and whisk. Then add in the eggs, one at a time, until incorporated. Then add in the vanilla.
1/2 cup brown sugar, tightly packed (light or dark), 1/3 cup white sugar, 1 large egg, room temperature, 1 large egg yolk, room temperature, 1 tsp. vanilla extract
Add in the dry ingredients (including the pulsed oats) and fold them in just until incorporated. The dough may feel or look wet, but as it sits the flour will hydrate and it will feel more like a cookie dough.
3/4 cup all-purpose flour, spooned and leveled, 3/4 cup cake flour, spooned and leveled, 1 tsp. cornstarch, 1/2 tsp. baking soda, 1/2 tsp. baking powder, 1/2 tsp. salt, 1 tsp. ground cinnamon, 1/2 tsp. ground nutmeg
Roll into about 1 - 1 1/2 Tbsp. sized balls and place on the prepared cookie sheets.
Bake for ~8-10 minutes or just until the edges are golden brown. Be careful not to over bake, under bake is key. Let the cookies cool on the cookie sheet for 5 minutes then transfer to a wire cooling rack.
Make the frosting: whisk all frosting ingredients together in a bowl. The frosting will be thick, this is perfect (add more powdered sugar as needed to get right consistency). Dip/dunk the tops of each cooled cookie lightly into the frosting. Repeat with remaining cookies and enjoy!
1 cup powdered sugar, or more as needed, 2 Tbsp. milk, 1/2 tsp. vanilla extract, pinch of salt