In the bowl of a stand mixer fitted with a paddle attachment or a large bowl, beat together the butter, brown sugar, and granulated sugar until smooth and creamy.
Beat in the eggs, one at a time, followed by the vanilla extract.
Pulse in the dark cocoa powder until incorporated.
In a medium bowl, combine the all purpose flour, cake flour, cornstarch, baking powder, baking soda, and salt.
Mix the flour mixture into the butter until just combined.
Stir in 9 ounces (255 grams) of the chocolate chips.
Pull off about 1/3 cup piece of dough, weighing it and adding more or less to make 4.5 ounces (128 grams).
Roll into a ball and place on a parchment-lined baking sheet. Repeat with the remaining dough, dividing them between two baking sheets and about 2-3 inches (5-7.5 centimeters) apart.
If desired, top the cookie balls with the remaining 3 ounces (85 grams) chocolate chips.
Place the baking sheets in the freezer for 1 hour to thoroughly chill.
Preheat oven to 350˚F (180˚C).
Bake the frozen cookies in the preheated oven until just set, about 18 minutes.
Allow to cool to room temperature, about 20 minutes, before serving. These cookies are best served the day they are baked.