Preheat oven to 350°F (177°C). Spray a 9-inch pie dish or 9-inch round cake pan with nonstick spray. Set aside.
In a large bowl using a handheld mixer or stand mixer fitted with paddle attachment, beat the butter for 1 minute on medium speed until completely smooth and creamy. Add the brown sugar and beat on medium speed until creamy, about 1 minute. Mix in egg, egg yolk, and vanilla on medium-high speed until combined. Scrape down the sides and bottom of the bowl as needed.
In a separate bowl, combine flour, cornstarch, baking soda and salt. On low speed, slowly mix into the wet ingredients until combined. The cookie dough will be quite thick. Add 1 and 1/4 cups chocolate chips and mix for about 5 seconds until evenly disbursed.
Press the cookie dough evenly into the prepared pan. Bake for 20-25 minutes or until the cake is lightly golden brown (could be up to 30 minutes, depending on your oven). Use a toothpick to test for doneness. You may want to cover the cake loosely with aluminum foil after 15 minutes to avoid heavy browning around the edges. Remove from the oven and set the pan on a wire rack to cool completely. Once cooled, use a sharp knife or metal spatula to loosen the sides of the cookie cake from the pan and transfer to a serving dish. (Or use can serve directly from the pan.)
Decorate the cooled cookie cake with frosting and remaining 1/4 cup chocolate chips. Depending how much frosting you use, you may have some leftover. I used a Wilton 1M tip. Cookie cake remains fresh covered tightly at room temperature for up to 3 days.
