Line a 9 x 13-inch pan with nonstick foil or regular foil and spray the foil with nonstick cooking spray; set aside.
Preheat the oven to 350°F (177°C).
Brown 2 sticks of butter in a saucepan over medium heat, stirring frequently, until it develops a nutty aroma and brown flecks; remove from heat and let cool to room temperature.
In a large bowl, cream the cooled brown butter with 3/4 cup brown sugar and 3/4 cup white sugar until combined and slightly fluffy.
Add 2 eggs and 2 teaspoons vanilla to the butter-sugar mixture and beat until fully incorporated.
Stir in 2 1/2 cups flour, 1 teaspoon baking soda, and 1 teaspoon salt until just combined; do not overmix.
Fold in the 12 ounces chopped chocolate, reserving a few chunks to press on top if desired.
Press the dough evenly into the prepared pan and arrange reserved chocolate pieces on top.
Bake for 25–30 minutes, until the edges are golden and a toothpick inserted into the center comes out with a few moist crumbs.
Allow the bars to cool completely in the pan, then lift out using the foil and cut into bars.