Whisk the flour, cornstarch, baking soda, and salt together in a medium bowl. Set aside.

In a large bowl using a hand mixer or a stand mixer fitted with a paddle attachment, beat the cream cheese on medium-high speed until completely smooth and creamy. Add the butter and beat until combined, scraping down the sides and up the bottom of the bowl as needed. Add granulated sugar and brown sugar and beat on medium-high speed until smooth and creamy, about 2 minutes. Add the egg and vanilla and beat on high speed until combined, about 1 minute. Scrape down the sides and up the bottom of the bowl and beat again as needed to combine.

Add the dry ingredients to the wet ingredients and mix on low speed until combined. With the mixer running on low speed, beat in the white chocolate chips. Add the Oreos and beat on low speed or gently fold in with a silicone spatula or wooden spoon until combined. Cover and chill the dough for at least 2 hours in the refrigerator (and up to 4 days).

Preheat oven to 350°F (177°C). Line baking sheets with parchment paper or silicone baking mats. Set aside.

Roll cookie dough, a heaping 1.5 Tablespoons of dough per cookie, and place 3 inches apart on the baking sheets. Bake for 12–13 minutes or until lightly browned on the sides. The centers will look very soft.

Remove from the oven and allow cookies to cool on the baking sheet for 5 minutes before transferring to a wire rack to cool completely.