Heat the butter in a heavy-bottomed saucepan until it is all melted, darker in color, and the milk solids are caramelized. The butter should smell nice and nutty.
Allow to cool to room temperature.
Mix together the flour, cornstarch, baking soda, and salt together in a small bowl and set aside.
Beat the butter and both sugars until well-combined about 4 - 5 minutes on medium speed. The mixture will look like very wet sand
Add in the egg, yolk, and vanilla. Beat well until well-combined, at least another 2 - 3 minutes. The mixture should come together to a smooth, almost creamy consistency.
Stir in the flour mixture and mix until just combined,
Chill the dough for at least an hour, preferably 24 - 72 hours for the best flavor development.
Portion the cookie dough into balls and set aside to rest while the oven preheats.
Preheat the oven to 350°F. Line two baking sheets with parchment paper.
Place the cookie dough 2-inches apart on your baking sheets and bake for 8 - 10 minutes, or until golden brown.
Allow the cookies to rest on the baking sheet for 1 -2 minutes before transferring to a wire rack to cool completely. Top with flaky sea salt while still warm.