Preheat oven to 350°F (177°C). Grease 3 6-inch cake pans, line with parchment paper, then grease the parchment paper. Parchment paper helps the cookie cakes seamlessly release from the pans.
Whisk the flour, cornstarch, baking soda, and salt together in a medium bowl. Set aside.
In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the butter, brown sugar, and granulated sugar together on medium-high speed until smooth and creamed, about 2 minutes. Add the eggs and vanilla extract and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine.
Add the dry ingredients to the wet ingredients and mix on low until combined. With the mixer running on low speed, beat in the chocolate chips. Dough will be thick and sticky.
Divide cookie dough between however many cake pans you're using. Press evenly into each. If baking in batches, cover any cookie dough that isn't being used and set aside at room temperature.
Bake for 20-22 minutes or until the cake layers are lightly brown on top and a toothpick inserted in the center comes out mostly clean. Allow cakes to cool for 10 minutes in the pans. Run a sharp knife around the edges, then carefully invert the pan so the warm cookie cake slides out. (At this point you can clean out pans, grease, line with parchment, grease parchment, then bake remaining cakes if needed.) Set the baked cakes on a wire rack to cool completely. The cakes must be completely cool before frosting and assembling.
Cover leftover cake tightly and store in the refrigerator for 5 days.