Prepare brown butter: In a medium saucepan, melt the butter over medium heat. Once it bubbles vigorously, cook 6–8 minutes, swirling occasionally, until bubbles subside, foam forms, and toasty brown flecks appear. As soon as you get these visual cues and a nutty fragrance, pour the butter into a heatproof bowl, scraping the bottom of the bowl, and allow to cool for at least 30 minutes. You'll have around 240g of brown butter.
In a medium bowl, whisk together flours, salt, baking powder, and baking soda.
Using the paddle attachment of a stand mixer, mix together both sugars and the cooled brown butter for about 30 seconds to combine.
Add eggs one at a time and the vanilla, mixing thoroughly after each addition, and scraping the bowl halfway through, then again after you've added the last egg.
Mix in the flour mixture until just barely incorporated with floury bits remaining, then paddle in the chocolates until evenly mixed. Use your hand or a spatula to scrape the bottom of the bowl to ensure no gooey bits remain.
Portion the cookies into 100g balls, and rest, covered, in the fridge overnight.
The next day, preheat the oven to 180℃/350℉, and bake the cookies for about 17-18 minutes, rotating halfway through baking.
Sprinkle generously with flaky salt as soon as they come out of the oven and enjoy!
