Line a large cookie sheet with parchment paper and set aside.
Melt the unsalted butter in a medium saucepan over medium heat, stirring occasionally until golden brown.
Pour the browned butter into a large mixing bowl and let it cool for about 20 to 25 minutes.
Pulse the old-fashioned oats in a food processor until you have a mix of fine crumbs and larger pieces.
In a separate bowl, whisk together the all-purpose flour, baking soda, ground cinnamon, and salt.
Add granulated sugar and light brown sugar to the cooled butter, whisk until combined, then add egg and vanilla.
Fold the dry mixture and processed oats into the wet ingredients until just combined.