Preheat the oven to 350°F. Line the bottom and sides of a 9- x 9-inch baking pan with aluminum foil or parchment, leaving an overhang on all sides to easily lift the bars out of the pan when cool. Set aside.
In a saucepan with a heavy bottom, melt the butter on medium-high heat. Continue cooking the butter until it turns amber and smells nutty, about 8 minutes. Immediately remove the pan from the heat and pour butter into a bowl to stop the cooking process. Let cool slightly.
Whisk the flour, baking soda, cornstarch, and salt together in a large bowl. Set aside.
In a medium bowl, whisk the melted brown butter, brown sugar, and granulated sugar together until no brown sugar lumps remain. Whisk in the egg, then the egg yolk. Finally, whisk in the vanilla extract. The mixture will be thick. Pour the wet ingredients into the dry ingredients and mix together until combined. The dough will be very soft, yet thick. Fold in the chocolate chips. The chips may not stick to the dough because of the melted butter but do your best to combine them.
Transfer dough to the prepared baking pan and press/smooth into an even layer. Sprinkle the top with sea salt if desired. Also, press a few more chocolate chips on top of the dough before baking (just for looks). Bake for 32-35 minutes or until lightly browned on the sides. Use a toothpick to test for doneness; if it comes out clean from the center of the pan, the bars are done.
Allow the bars to cool in the pan set on a wire rack for at least an hour. Once relatively cool, lift the foil out of the pan using the overhang on the sides and cut into bars. Store in an airtight container at room temperature for up to a week.