• Preheat oven to 350°F. Lightly grease a 10-inch round cake pan or springform pan and line the bottom with parchment paper. Set aside.

Make The Chocolate Chip Cookie Cake:

• In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth and creamy, about 1 minute.
• Add the brown sugar, granulated sugar, and vanilla. Beat on medium speed until light and fluffy, about 2-3 minutes, scraping down the bowl once.
• Add the egg and beat just until combined. Add the egg yolk and beat again just until combined.
• In a separate bowl, whisk together the flour, cornstarch, baking powder, and salt.
• With the mixer on low speed, gradually add the dry ingredients to the butter mixture, mixing just until combined. Stop and scrape down the sides and bottom of the bowl as needed. The dough will be thick.
• Use a spatula or wooden spoon to gently fold in the chocolate chips until evenly distributed.
• Transfer the dough to the prepared pan. Press it into an even layer, smoothing the top and pushing the dough all the way to the edges.
  
• Bake for 22-28 minutes, or until the edges are lightly golden brown and the center looks set but still slightly soft; a toothpick inserted near the center should come out mostly clean, with a few moist crumbs.
  
• Place the pan on a wire rack and let the cookie cake cool completely in the pan, about 1 to 1 1/2 hours. Once cool, run a thin knife around the edges to loosen, then carefully remove the outer ring or invert onto a plate and flip right-side up onto a serving platter.
  

Make The Buttercream Frosting:

• In a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, beat the butter on medium speed until smooth, pale, and creamy, about 2-3 minutes.
• Add half of the powdered sugar and beat on low speed until incorporated, then increase to medium and beat until smooth.
• Add the remaining powdered sugar, vanilla, salt, and 1 tablespoon of milk or cream. Beat on medium speed until light and fluffy, about 2 minutes, adjusting the speed as needed to keep the sugar from puffing out.
• If the frosting is too stiff, add up to 1 additional tablespoon of milk or cream, a little at a time, and beat until smooth. If it seems too soft for piping, beat for another minute or add a spoonful of powdered sugar.

Finish And Serve The Dish:

• Spoon the frosting into a piping bag fitted with a star tip. Pipe around the edges of the cooled cookie cake.
  
• Decorate with colorful sprinkles, if desired. Serve immediately or store in an airtight container.