Preheat your oven to 400°F. Line two baking sheets with parchment paper.

Using a mixer, beat the cold butter with brown sugar and granulated sugar until creamy.

Add the egg and egg yolk, and mix until well combined.

Mix in vanilla extract.

Whisk together the flour, cake flour, salt, baking powder, and baking soda in a bowl.

Gradually add dry ingredients to wet mixture, mixing on low speed.

Stir in the chocolate chips and peanut butter chips.

Shape the dough into 8 large balls and place them on the baking sheets.

Bake for 12 minutes, until edges are golden brown.

Cool on sheets for 10 minutes before transferring to a wire rack.

Serve warm or at room temperature.