Preheat the oven to 350 degrees. Using a stand mixer, cream the butter, sugar, brown sugar for 3-4 minutes. Since the butter is cold, you want to mix the sugars and butter for quite a bit until it's all combined.
Add the eggs and vanilla and continue to mix for an additional minute.
Add in the cake flour, all-purpose flour, cornstarch, baking soda, and salt. Mix until just blended. No need to overmix.
Stir in chocolate chips by hand.
Use parchment paper or a silpat mat to line a baking sheet. Scoop about 2-3 tablespoon scoops of dough onto the baking sheet. Keep the dough balls all the same size for even baking.
Bake for 9-11 minutes. Remove from oven and let set on the baking sheet for 10 minutes to set.