In a medium bowl, whisk together the flour, cornstarch, baking soda, and salt. Set aside.
In the bowl of a stand mixer fitted with the paddle attachment, or in a large bowl if using an electric hand mixer, beat the cream cheese over medium-high speed, until creamy and smooth. Add the softened butter and beat until nicely combined and creamy, scraping the sides and the bottom of the bowl with a spatula as needed.
Next, add the granulated sugar and the brown sugar and beat on medium-high speed until smooth and creamy, about 2 minutes.
Add the egg and the vanilla extract and mix until combined.
With the mixer on low speed, gradually add the flour mixture to the cream cheese mixture. Mix until combined.
Add the white chocolate chips and using a spatula or a wooden spoon, mix them into the dough. Next, add the Oreo chunks and gently fold them in until combined.
Wrap the cookie dough with plastic wrap and refrigerate dough, for 2 hours or up to 4 days. The cookie dough must be chilled before you bake the cookies. This dough is soft and will spread out if skipping this step.
Preheat the oven to 350°F (177°C). Line 2 baking sheets with parchment paper and set aside. You can use silicone mats also.
Scoop about 1 ½ heaping tablespoons of cookie dough per cookie, and place them on the prepared baking sheet leaving 3 inches between each cookie scoop.
Bake for 12–13 minutes or until the edges are lightly browned and the centers look very soft.
Remove from the oven and allow the cookies to cool on the baking sheet for 5 minutes. Transfer to a wire rack to cool completely.