Combine the all purpose flour, baking soda, salt, and cornstarch in a small bowl and whisk them together.
Using a mixer with a paddle attachment, cream the softened butter, white sugar, and brown sugar on medium speed until the mixture is light and fluffy.
Add the whole egg, egg yolk, and vanilla extract to the butter mixture and beat again until fully incorporated and smooth, scraping down the sides of the bowl as needed.
Gradually add the dry ingredients to the wet ingredients, mixing until a soft dough has formed.
Fold in the chopped Oreos along with the white chocolate chips and semi sweet chocolate chips evenly through the dough, then let it rest at room temperature for 20 minutes.
Preheat your oven to 350°F (175°C) and line a baking sheet with parchment paper.
Portion the dough using a large ice cream scoop or tablespoon into balls sized about 1/4 to 1/3 cup, spacing them evenly on the prepared baking sheet, about 6 per tray.
Bake for 11 to 12 minutes, or until the edges appear golden while the centers remain slightly soft.
Remove the cookies from the oven and allow them to cool on the baking sheet for about 10 minutes to firm up before transferring them to a wire rack to cool completely.
Enjoy your homemade chewy and crispy Cookies Cream Cookies fresh or store in an airtight container to keep them soft.