Melt the butter in a saucepan over medium heat until golden brown and fragrant, then let it cool for 20 minutes.
Preheat the oven to 350°F (175°C) and line baking sheets with parchment paper.
Beat the cooled brown butter, brown sugar, and granulated sugar until smooth.
Mix in the eggs one at a time, then stir in the vanilla extract.
Whisk together the flour, oats, baking soda, cinnamon, salt, and baking powder in a separate bowl.
Gradually add the dry ingredients to the wet ingredients until just combined.
Fold in the chopped nuts if using.
Scoop tablespoon-sized portions of dough onto the prepared baking sheets.
Bake for 10–12 minutes until the edges are golden and the centers are just set.
Cool on the baking sheet for 5 minutes before transferring to a wire rack.