Preheat your oven to 400 degrees F. Line a baking sheet with parchment paper and set aside.
In a medium size bowl, whisk together the all-purpose flour, cake flour, baking powder, baking soda, and salt. Set aside.
In another medium size mixing bowl, beat the butter, granulated sugar, brown sugar, and lemon zest until light and fluffy, about 2 minutes.
Add the egg, egg yolk, and lemon extract. Beat until combined.
Slowly add the flour mixture and stir on low until incorporated.
Fold in the white chocolate chips.
Measure the dough into 6 ounce balls. Place four balls of dough on the baking sheet and bake for about 12 minutes. The outside of the cookie should be golden brown.
Allow to cool to room temperature before eating. (This allows the middle to set properly).