Preheat oven to 400°F and line two baking sheets with parchment paper. In a medium bowl, whisk together all-purpose flour, cake flour, cornstarch, baking powder, baking soda, and salt. Set aside.
Cream cold butter in stand mixer with paddle attachment on medium-low for 30 seconds. Add brown sugar and mix 30 seconds, then add granulated sugar and mix 30 more seconds until combined.
Add egg and egg yolk one at a time, mixing until just incorporated. Scrape down bowl. Mix in vanilla extract if using.
Add dry ingredients in two additions on low speed, mixing just until no dry streaks remain. Fold in chocolate chips by hand with rubber spatula.
Portion dough into 6 large balls (3-4 oz each). Place on baking sheets 3 inches apart. Chill at least 2 hours or overnight.
Bake at 400°F for 5 minutes, then reduce to 375°F and bake 7-10 more minutes until edges are set but centers look slightly underbaked.
Cool on pan 5 minutes, then transfer to wire rack. Sprinkle with sea salt flakes if desired. Serve warm or store in airtight container.