Preheat oven to 350F (175C) and prepare a 10" round pan by lining the bottom with parchment paper or by lightly greasing. Set aside.
combine softened butter and sugars in a large bowl and use an electric mixer to beat well until light and fluffy.
Add eggs, and egg yolk one at a time, stirring well after each addition.
Stir in vanilla extract.
In a separate, medium-sized bowl, whisk together flour, cornstarch, baking powder, and salt.
Gradually stir dry ingredients into wet until completely combined. Stir in chocolate chips and sprinkles.
Spread batter evenly into prepared pan. Bake on 350F (175C) for 30 minutes or until edges just begin to turn golden brown.
Prepare chocolate frosting while the cookie cake cools.
Cream butter with an electric mixer.
Gradually add sugar until completely combined
Stir in cocoa powder and then vanilla extract. Pause to scrape down the sides of the bowl with a spatula.
Add milk (start with just 1 teaspoon, if consistency is still too stiff add another) and beat well
Pipe icing around the rim of your cooled cookie cake -- I used a piping bag fitted with a Wilton 2D tip, but in a pinch you can simply transfer your frosting to a ziploc bag, snip off a small corner, and pipe that way.