Line a square 8x8 baking pan with parchment paper to cover all four sides. Preheat the oven to 350 F/180 C.
In a stainless steel or light-colored pan, cook the butter over medium heat, stirring occasionally for 10-11 minutes, or until it smells nutty and there are amber brown bits of butter solid at the bottom of the pan. As the butter browns, it will pop, foam, and bubble. Stand nearby and watch it carefully so it doesn’t burn! Scrape the browned butter into a container with a spout for pouring. Set aside to cool for 20-30 minutes, or until it feels warm but isn't hot or it will melt the chocolate.
In a large bowl, whisk together the sugars, eggs, egg yolk, and vanilla, until light and pale in color, about 1 minute.
Slowly stream the brown butter into the bowl, whisking constantly to combine.
Fold in the flour and salt until most combined, then add in the chocolate chips and continue mixing until just combined.
Spread the batter into the prepared baking pan.
Bake for 28-35 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs.
Let the pan cool completely on a wire cooling rack before cutting, then enjoy!