Preheat oven to 350° F. Coat a 9 inch cake pan with cooking spray and line the bottom of the pan with a circle of parchment paper. Set aside.
In the bowl of a stand mixer fitted with paddle attachment, beat the butter for at medium speed for 2-3 minutes or until light and fluffy. Add the brown sugar and granulated sugar and beat for 1 more minute. Add the egg, egg yolk and vanilla and beat for 1 minute. Scrape down the sides and bottom of the bowl with a spatula if needed.
Combine the flour, baking soda, salt and corn starch in a medium bowl. Add the dry ingredients to the butter mixture and mix on low until just combined. Stir in 1 cup of chocolate chips.
Press the cookie dough evenly into the prepared pan. Sprinkle the remaining 1/2 cup of chocolate chips over the top of the cookie dough.
Bake for 22-24 minutes or until the cake is golden brown at the edges. Place the pan on a cooling rack. Cool for 5 minutes then run a thin knife or spatula along the edge of the pan to loosen.
Once the cookie cake has completely cooled, carefully invert the cake pan onto a plate, then gently flip the cookie right side up.
For the frosting: In the bowl of a stand mixer fitted with a paddle attachment, beat the butter on medium speed until creamy - about 2-3 minutes.
Add the cocoa powder and powdered sugar and mix on low speed until just combined. Add the milk and vanilla then beat at medium speed until frosting is smooth and creamy, 2-3 minutes.
Pipe the frosting onto the edge of the cake and then decorate with the rainbow sprinkles. Place in the refrigerator until 30 minutes before it's time to serve the cake.