Melt the butter in a medium-sized pan over medium heat, stirring constantly to prevent burning. Once browned, remove from heat and transfer to a glass bowl, allowing it to cool for 30 minutes.
Preheat your oven to 350°F (175°C) and line a baking tray with parchment paper.
In a large bowl, whisk together the cooled brown butter with light brown sugar and white sugar until well combined.
Add in the room temperature egg and vanilla extract into your sugar mixture. Whisk thoroughly until everything is well combined.
Gently fold in all-purpose flour, baking soda, and salt (if using) into your wet mixture until almost combined.
Lastly, add in the chopped dark chocolate and finely chopped roasted pistachios. Continue folding until no flour streaks remain visible.