Preheat oven to 350 degrees F. Line a large baking sheet with parchment paper and set aside.

Melt butter in a medium skillet or pan over medium heat. After a few minutes, the butter will begin to crackle and then foam. Make sure you whisk consistently during this process. After a couple of minutes, the butter will begin to brown on the bottom of the saucepan. Continue to whisk and remove from heat as soon as the butter begins to brown and give off a nutty almost hazelnut-like aroma. Immediately transfer the butter to a bowl to prevent burning but make sure you scrape all the yummy brown bits from the pan; this is where the flavor is! Set brown butter aside to cool for 5 minutes.

With an electric mixer, mix the brown butter and sugars until well combined, about 1 minute. 

Beat in the egg and vanilla until smooth and creamy, about 1 minute. 

Add the dry ingredients: flour, oats, baking soda, cinnamon, nutmeg and salt; beat on low speed until just combined.

Use a medium cookie scoop or your hands to grab about 1 large teasing tablespoon of dough. Drop on prepared cookie sheet, leaving at least 2 inches of space between each cookie. 

Bake for 10-13 minutes or until golden brown on the edges. Allow cookies to cool on the cookie sheet for a few minutes before transferring to a wire rack to finish cooling.

When cookies are baking, you can make the icing: Add powdered sugar, vanilla extract and milk to a medium bowl and mix until smooth and no visible lumps. 

Once cookies have cooled a bit, spoon two teaspoonfuls of icing onto each cookie and spread out a little, then return to wire rack to let the icing harden. Makes about 2 dozen cookies (24).