Cook the unsalted butter for 5-6 minutes until it turns golden and smells nutty, watching for brown flecks at the bottom. Remove from heat and let it cool for 15 minutes until warm but not hot (the color should stay amber).

Preheat the oven to 350°F and line a 9x13-inch pan with parchment. Lightly press the parchment into the corners so the bars lift out cleanly.

Whisk the brown butter with the brown sugar, then whisk in the granulated sugar until glossy and smooth. Scrape the sides to make sure no dry pockets remain.

Whisk in the eggs one at a time, then stir in the vanilla extract until the batter looks thick and cohesive. The mixture should turn slightly lighter in color as it combines.

Stir in the all-purpose flour, baking soda, and salt, then fold until just combined. Stop mixing as soon as no dry flour streaks remain, then fold in the semi-sweet chocolate chunks.

Spread the dough evenly into the prepared pan, pressing into the corners for uniform thickness. Aim for a level surface so the tops bake crackly all over.

Bake at 350°F for 22-25 minutes until the edges are golden and the center is just set. Look for a slightly puffed top with darker golden edges.

Sprinkle flaky sea salt over the warm bars, then cool completely before cutting. The bars should feel firm when pressed lightly at the center.