In a stand mixer fitted with a paddle attachment, cream together butter and sugar for 8 minutes, until it is light and fluffy and resembles whipped butter.
Add vanilla, egg, and egg yolks. Mix on medium-low speed until combined.
Add all-purpose flour, cake flour, salt, baking soda, baking powder, and cornstarch. Mix on low speed until combined or about 1 minute.
Fold in the chocolate chips.
Scoop dough into 150g/ 4oz balls (about ½ cup) and place on a parchment-lined tray. Cover and freeze for at least 1 hour or overnight.
When ready to bake, preheat the oven to 425℉/220℃.
Place 6 frozen dough balls on a baking sheet, evenly spaced, lined with parchment paper. Sprinkle each cookie with flaky salt, and bake for 20 minutes at 425°F/ 220℃ until golden, rotate the tray every 7 minutes.
When the cookies are fully golden brown all over and set, remove from the oven and allow to rest for about 5 minutes before moving them over to a cooling rack. Enjoy the cookies warm for best gooey results.