Preheat the oven to 400°F. Whisk together the All-purpose flour, cake flour, baking soda, baking powder, cornstarch and salt together in a large bowl. Set aside.
Place the cubed butter into the bowl of a stand mixer and secure the paddle attachement. Turn the mixer on a medium-low setting.
Let the mixer cream the butter for 30 seconds, and then add in the brown sugar and mix 30 seconds, followed by the white sugar for 30 seconds. Cream until light and fluffy, then add in the egg and the egg yolk (and vanilla if using) and blend until mixed. If any of the butter gets stuck on the paddle attachment use a rubber spatula to knock it off.
With the mixer on low speed, gradually add in the flour mixture. Add it in a little at a time until ingredients are incorporated. Then add in the chocolate chips and mix just until the chocolate chips are incorporated. Turn off the machine.
Measure out ~6, 5.7 oz. cookies. I like to use a food scale for this but if you don't have one, simply eye-ball it. Cookies will be a little smaller than a fist, huge I know! Keep the cookies nice and tall and don't flatten them. Place cookies on a cookie sheet. You can use a silicone baking mat or parchment paper if you prefer.
Bake cookies for 10-12 minutes or until the tops are golden brown. The secret is to pull them out before you think they are done. (See recipe notes if your cookies are gooey)
Let them rest on the cookie sheet for at least 15-30 minutes. It's hard to wait. Trust me, I've been there. Place the cookies on a cooling rack to finish cooling completely. Enjoy with a big tall glass of milk!