In a medium bowl whisk together all-purpose flour, cake flour, cornstarch, baking soda, baking powder, and salt.
In a separate large bowl whisk melted butter, brown sugar, and granulated sugar until smooth and glossy.
Add egg, egg yolk, and vanilla extract. Mix until combined.
Add dry ingredients into the wet ingredients and mix until just combined. Do not overmix.
Fold in crushed Oreos and white chocolate chips.
Scoop large dough balls (about 5–6 oz each).
Flatten dough in your hand.
Place a whole Oreo cookie in the center of the dough.
Wrap dough around filling and seal completely.
Roll into tall dough balls rather than flattening.
Place assembled cookie dough balls in the refrigerator for 45–60 minutes. This helps create thick NYC-style cookies.
Preheat oven to 375°F.
Line baking sheet with parchment paper.
Bake cookies for 12–14 minutes.
Edges should be set and centers slightly underbaked.
Let cookies cool on the baking sheet for 10 minutes before moving.