Brown the Butter: In a saucepan over medium heat, melt the butter. Continue cooking, swirling the pan occasionally, until the butter begins to brown and emit a nutty fragrance. Be careful not to burn it! Once browned, transfer the butter to a heatproof bowl and chill it in the fridge for about 10 minutes. It should still be soft enough to mix but slightly solidified.
Make the Cookies: While the butter chills, preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper. In a separate bowl, whisk together the flour, cornstarch, baking soda, and salt. Set this mixture aside. Once the browned butter is ready, beat it together with the brown sugar and granulated sugar until the mixture becomes light and fluffy. Mix in the egg, egg yolk, heavy cream, and vanilla extract until well combined. Gradually add the dry ingredients to the wet mixture, stirring just until everything is incorporated. Gently fold in the chocolate chips and the chopped semi-sweet chocolate bar, distributing them evenly throughout the dough. Tightly wrap the dough in clingwrap and chill in the fridge for up to 48 hours (minimum of 30 minutes).
Scoop the cold cookie dough onto the prepared baking sheet, leaving enough space between each cookie for them to spread. Bake in the preheated oven for 10-12 minutes, or until the edges are golden but the centers still look soft. Allow the cookies to cool on the baking sheet for a few minutes before transferring them to a wire rack to cool completely. Enjoy the rich, decadent flavor of browned butter in every bite!
