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.¾ cup (170 g) unsalted butter, ¾ cup (150 g) light or dark brown sugar, ⅔ cup (135 g) sugar
Add egg, egg yolk, and vanilla extract and stir well.1 egg + 1 egg yolk, 1 teaspoon vanilla extract
In a separate, medium-sized bowl, whisk together flour, cornstarch, baking powder, and salt.2 cups (250 g) all-purpose, 1 ½ teaspoon corn starch, ½ teaspoon baking powder, ¾ teaspoon salt
Gradually stir dry ingredients into wet until completely combined. Stir in chocolate chips and sprinkles.1 cup (170 g) semisweet chocolate chips, 2 Tablespoons 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.
Chocolate FrostingBeat butter with an electric mixer until smooth and creamy.½ cup (113 g) 1 stick salted butter, softened to room temperature
Gradually add sugar until completely combined1 ½ cups (188 g) powdered sugar
Stir in cocoa powder and then vanilla extract. Pause to scrape down the sides of the bowl with a spatula.¼ cup (25 g) cocoa powder, ½ teaspoon vanilla extract
Add milk (start with just a splash, if consistency is still too stiff add more as needed until you have a smooth creamy consistency) and beat well1-2 Tablespoons milk
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.
Slice and enjoy!