Preheat the oven to 350°F. Grease an 8 or 9 inch cake pan and set aside.
In a medium bowl, cream together the brown sugar, sugar, butter, and vegetable oil. Add the egg and vanilla, and beat until light and fluffy. Add the baking soda, salt, baking powder, and flour, and mix until just combined. Fold in the chocolate chips.
Spread the cookie dough in the prepared cake pan. Bake 22-25 minutes, until lightly browned around the edges. Remove from the oven and let cool completely.
To make the frosting, beat together the butter, cocoa powder, and powdered sugar. Add the vanilla and 1 tablespoon of milk, and beat until smooth. Add additional milk as needed to make a fluffy and smooth frosting.
To decorate the cookie cake, pipe dollops of chocolate frosting on the top of the cookie using a large open star tip. Sprinkle with colorful sprinkles.