In a stand mixer with the paddle attachment or a large mixing bowl, cream together the cold cubed Unsalted Butter (1 cup), Brown Sugar (1 cup), and Granulated Sugar (1/2 cup). Cream on medium for about 2-4 minutes until creamy and combined. You want just a few small pieces of butter to remain.
Add Vanilla Extract (1 teaspoon) and Egg (2), one at a time, mixing until combined.
Add All-Purpose Flour (1 1/2 cup), Cake Flour (1 1/2 cup), Unsweetened Cocoa Powder (1/2 cup), Corn Starch (1 teaspoon), Baking Soda (1 teaspoon), and Kosher Salt (1 teaspoon). Mix until just combined and avoid over-mixing. Stir in the White Chocolate Chips (1 cup) and Semi-Sweet Chocolate Chips (1 cup). The dough will be thick.
Form the dough into thick hockey puck-like discs. Using 6 ounces (about 1/2 cup) of dough for each. The discs should be about 1 1/2 to 2 inches thick. Avoid overworking the dough, just gently press into shape.
Chill discs of dough in the fridge until firm, at least 30 minutes and up to 3 days.
Preheat oven to 400 degrees F (205 degrees C). I recommend using an oven thermometer to ensure an accurate and consistent temp. Line two light-colored baking sheets with parchment paper.
Working in batches, place a few chilled discs on a prepared baking sheet and bake for 14-17 minutes (mine baked for 15 minutes exactly). The cookies are done when they are puffy, golden on the outside, and set.
Allow them to cool on the sheet for 10 minutes before moving to a cooing rack. Repeat with the remaining cookies. Be sure to not place dough on a warm baking sheet – run hot sheet under cold water if needed to cool it down.
Enjoy! I like to give a light sprinkle of flaky salt before serving.