In a stand mixer, beat cold butter, granulated sugar, and brown sugar until light and fluffy, about 3-4 minutes.
Mix in eggs and vanilla extract, beating just until combined.
In a separate bowl, whisk together all-purpose flour, cake flour, baking soda, and salt. Slowly mix it into the butter mixture.
Gently fold in the chocolate chips until evenly distributed.
For thicker cookies, chill the dough for at least 30 minutes (or overnight for even better flavor).
Roll the dough into large balls, about ¼ cup per cookie, and place them on a parchment-lined baking sheet.
Preheat oven to 375°F (190°C). Bake cookies for 10-12 minutes until the edges are set but the centers are still soft.
Let the cookies cool on the baking sheet for 5 minutes before transferring to a wire rack.