Add 10 tablespoons of unsalted butter into a large frying pan and cook over medium heat until the butter melts, stirring occasionally. Continue cooking for another 2-5 minutes while stirring constantly and watching closely. The melted butter will start to foam on top, then the milk solids will begin to caramelize and turn brown in color. Once the little flecks of milk solids are medium brown (without crossing over into the burnt/dark brown territory), remove from heat and transfer to a glass container and allow to cool for about 5-10 minutes.
Preheat the oven to 350ºF (177ºC). Prepare a 8-inch square baking pan inch by spraying the sides with baking spray and lining the bottom with parchment paper, leaving a slight overhang for easy removal of the cookie bars later on.
In a large bowl, add the brown sugar and granulated sugar. Pour the brown butter on top and whisk together until uniform. Add the egg, egg yolk, and vanilla, then continue whisking until uniform. Whisk in the cornstarch, baking soda, baking powder, and salt.
Add the flour and use a silicone spatula to fold it in until smooth cookie dough forms. Reserve about 1/4 Cup of the chocolate chips and set them aside, then pour the remaining chocolate chips into the cookie dough and fold until evenly dispersed.
Add the cookie dough into the prepared pan and press it down in an even layer all the way to the edges. Sprinkle the reserved chocolate chips on top and press them in, then bake for 17-20 minutes, until evenly puffed and the edges are lightly golden. It might seem soft in the middle but don't be tempted to over-bake! It will continue to bake in the pan as it cools.
Let the cookie bars cool in the pan for about 30 minutes, then transfer to a wire rack to cool completely to room temperature before slicing into squares, or enjoy it warm after the 30 minute cooling time – either way is delicious!