Preheat your oven to 350°F (175°C).
In a mixing bowl, combine the melted butter, dark brown sugar, and white sugar. Mix until fully incorporated and smooth.
Add the small egg yolk and vanilla extract, stirring to blend until creamy.
in the same bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking soda, and kosher salt. (no need to dirty another bowl)
Gently combine ingredients, leaving a bit of flour streaks.
Fold in the milk chocolate chips and semi-sweet chocolate chips just until fully incorporated into your dough and you don’t see any more flour peeking through. Be careful not to over-mix.
Divide the dough into two equal portions, each weighing around 113 grams.
Roll each portion into a ball and place them on the prepared baking sheet, leaving enough space between them to spread.
Bake for 12-14 minutes, or until the edges are golden but the centers are still slightly soft. (it will set fully while it cools)
As soon as the cookies come out of the oven, sprinkle a bit of flaky salt on top.
Let the cookies cool on the baking sheet for a few minutes before transferring to a wire rack.
Enjoy immediately or, if one cookie is enough, freeze the other dough ball for a future treat or share with someone you love!