In a medium saucepan over medium heat, add the unsalted butter. Allow it to melt and continue cooking, stirring frequently, until it turns a golden brown and smells nutty, about 6-8 minutes. Remove from heat and let cool slightly.
In a large mixing bowl, combine the brown butter, dark brown sugar, and granulated sugar. Mix until well combined. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.
In another bowl, whisk together the all-purpose flour, kosher salt, baking soda, and baking powder.
Gradually add the dry ingredients to the wet mixture, stirring until just combined. Be careful not to overmix.
Gently fold in the chocolate chunks and chocolate chips, ensuring even distribution throughout the batter.
Preheat oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving overhang for easy removal.
Spread the cookie dough evenly in the prepared pan. Sprinkle flaky sea salt on top. Bake for 25-30 minutes, until edges are golden and a toothpick inserted comes out with a few moist crumbs.
Allow bars to cool in the pan for at least 15 minutes. Lift out using parchment paper and cool completely on a wire rack before slicing into squares.