Preheat your 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, cake flour, salt, baking powder, and baking soda.

With the mixer on low, gradually add the flour mixture to the wet ingredients. Mix until mostly incorporated.

Add the chocolate chips and peanut butter chips. Mix just until the flour is fully incorporated and the chocolate and peanut butter chips are evenly distributed.

Shape the dough into 8 large balls (about 6 ounces each).

Place 4 cookie dough balls on the prepared baking sheet, spacing them out evenly.

Bake in the preheated oven for about 12-13 minutes, or until the edges are golden brown.

Let the cookies cool on the baking sheet for 10 minutes before transferring to a wire rack.

Serve warm.