Preheat oven to 400°F (204°C). Line two baking sheets with parchment paper and set aside.
Using a stand mixer with the paddle attachment, combine cold butter, brown sugar, and granulated sugar. Beat on medium speed until no visible butter chunks remain and the mixture is creamy.
Add the egg and egg yolk and mix until combined. Add the vanilla extract and continue mixing, scraping down the sides of the bowl as needed, until combined.
In a medium bowl, whisk together flour, cocoa powder, salt, baking powder, and baking soda.
With the mixer on low, gradually add the flour mixture to the wet ingredients. Mix until mostly is incorporated.
Add the chocolate chunks, chocolate chips, and white chips. Mix just until the flour is fully incorporated and the chocolate pieces are evenly distributed.
Shape the dough into 8 large balls and place 4 on each prepared baking sheet, spacing them evenly.
Bake for 12-13 minutes, or until the edges are set and lightly golden.
Let the cookies cool on the baking sheet for 10 minutes. Then, transfer to a wire rack to cool completely.