In a medium bowl, whisk together the all-purpose flour, cake flour, cornstarch, baking powder, and salt. Set aside.

Place the cold butter pieces, granulated sugar, and brown sugar in the bowl of a stand mixer fitted with the paddle attachment. Mix on medium-low speed for about 2 minutes, stopping to scrape the bowl as needed. Mix only until you can no longer see chunks of butter. Do not continue creaming until the mixture becomes light and fluffy. Overmixing will warm the butter and may cause the cookies to spread too much.

Add the whole egg, egg yolk, and vanilla. Mix on low speed just until combined, about 30 seconds. The mixture may not look as light or fluffy as traditional creamed cookie dough. That is okay.

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. Avoid overmixing once the flour has been added.

Portion the dough into 3-ounce (85g) pieces using a large cookie scoop or kitchen scale. Shape each portion loosely by hand, but do not roll it into a perfectly smooth ball. Gently dimple the top with your fingertips, then press a few extra chocolate chips into the surface.

Arrange the portions on a covered baking tray and refrigerate for at least 30 minutes. For the best flavor, texture, and thickness, chill the portioned dough overnight. The dough should be completely cold before baking.

Preheat the oven to 375°F. Line a light-colored baking sheet with parchment paper. Arrange the cold dough portions several inches apart so the cookies have room to spread.

Bake for 10 to 12 minutes, or until the cookies have spread but are not yet fully baked.

Remove the baking sheet from the oven. These cookies do not always bake into perfectly round circles, especially if the dough has warmed or the portions are particularly large. Place a large round cookie cutter, ring mold, wide glass, or small bowl around each cookie. Gently move it in a circular motion to nudge the soft edges into a round shape.

Reposition any chocolate chips that have slipped toward the sides. Add a few more chocolate chips and a sprinkle of flaky sea salt, if desired.

Return the pan to the oven and bake for another 4 to 6 minutes. The total baking time should be 15 to 18 minutes. The edges should look set, but the centers should remain soft.

Let the cookies cool on the baking sheet for at least 10 minutes before transferring them to a wire rack. They will be very soft while warm and will continue to set as they cool.