Preheat the oven to 350°F. Grease a 9-inch square baking pan with unsalted butter. (See Kelly’s Notes.)
In the bowl of a stand mixer fitted with the paddle attachment, cream together the butter, granulated sugar and brown sugar until light and fluffy, about 2 minutes.
Beat in the egg then beat in the vanilla extract.
Add the flour, baking soda, baking powder and 1/2 teaspoon kosher salt and beat just until combined.
Beat in the chocolate chips.
Spread the cookie dough into the greased pan in an even layer.
Bake the cookie cake until it is pale golden and barely set in the center, 15 to 18 minutes. (For a softer cookie cake, underbake it.)
Remove the cookie cake from the oven and let it cool completely. Once it has cooled, cut it into 1-inch cubes.
Add several cookie cubes to a serving glass, top with frosting and sprinkles, and serve.