Place butter in a medium saucepan over medium heat. Melt, then cook 5-7 minutes, swirling, until it foams and dark golden bits collect at the bottom and it smells deeply nutty. Immediately scrape into a large mixing bowl (brown bits included) and let cool 10-15 minutes until just warm to the touch.

Add packed brown sugar and granulated sugar to the bowl with the cooled butter. Whisk or stir vigorously for 1-2 minutes until glossy and slightly thickened, ensuring the sugar dissolves and the mixture cools further. This keeps your dough thick and ready for eggs.

Add the eggs and vanilla extract to the sugar-butter mixture. Whisk forcefully until completely homogenous and glossy, about 45-60 seconds. The dough should lighten slightly in color and look cohesive, with no visible streaks of egg.

Sprinkle the flour and salt evenly over the wet mixture. Switch to a silicone spatula and fold in just until most dry spots disappear, but some flour streaks remain. This helps prevent overmixing and keeps the bars tender instead of tough.

Add chopped chocolate to the dough and fold gently just until chocolate is distributed and no dry flour remains. Do not overmix, stop as soon as the dough is cohesive and chocolate is well dispersed. The dough will be thick and a little sticky.

Line an 8x8-inch metal baking pan with parchment, leaving overhang on two sides. Scrape dough in and pat evenly to all corners using your spatula or fingers. Press a few extra big chocolate pieces on top for a bakery-style finish, if you like.

Bake at 350°F (175°C) for 25-28 minutes, rotating pan halfway. The top should be golden brown and edges look set, but the center should still appear slightly underdone and soft. Overbaking will yield dry edges and a cakey crumb.

Set pan on a wire rack and allow bars to cool completely, about 1-1.5 hours. For clean cuts, lift bars out with parchment, transfer to a cutting board, and use a sharp knife to slice, wiping knife between cuts for tidy edges.