Brown the butter: melt it in a light colored pan over medium heat, swirling often. It will foam, then turn golden with toasty brown flecks and a nutty smell, about 5-7 minutes.
Immediately pour it into a large bowl, including all the flecks, and cool for 10 minutes. Preheat your oven to 350°F and line an 8x8 inch pan with parchment paper.
Whisk the brown sugar into the browned butter for 1 minute until glossy, then whisk in the milk and vanilla.
Fold in the flour, cornstarch, baking powder, and salt just until no dry streaks remain.
Fold in the white chocolate chips, spread the thick batter into the pan, and scatter a few extra chips and flaky salt on top.
Bake for 22-26 minutes, until the edges are golden and the center is just set. A slightly underbaked center is what makes them chewy.
Cool completely in the pan, about 1 hour, before slicing into 16 squares.
