In a medium bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking powder, baking soda, and salt. Set aside.
Place the cold butter pieces in the bowl of a stand mixer fitted with the paddle attachment. Beat on low to medium-low speed just until the butter becomes pliable and begins to soften slightly, but is still cool.Add the granulated sugar and brown sugar. Mix on medium-low speed, stopping to scrape the bowl as needed, just until there are no large chunks of butter remaining. Do not cream the mixture until light and fluffy.Add the egg and mix on low speed just until combined and no glossy streaks of egg remain. Avoid overmixing. The goal is to bring the ingredients together without warming or aerating the butter too much. Add the dry ingredients. Mix on low speed until the flour is almost incorporated.
Add the chocolate chips and continue mixing just until the dough comes together.
Scoop the dough into 2-ounce portions. You should get about 14 to 16 cookies, depending on how evenly the dough is portioned.
Bake at 350°F for about 15 minutes, or until the edges are set and lightly golden while the centers still look soft.If baking the dough straight from the refrigerator, add about 3 to 4 minutes to the baking time. For a perfect bakery-style look, add extra chocolate chips and a sprinkle of flaky sea salt about halfway through baking or immediately after the cookies come out of the oven. Let the cookies cool on the baking sheet for a few minutes before transferring them to a cooling rack.