In a medium-sized mixing bowl, whisk together the all-purpose flour, cornstarch, baking soda, and salt until evenly distributed. Set aside.
Using a hand mixer or a stand mixer fitted with a paddle attachment, beat the softened cream cheese on medium-high speed until completely smooth and lump-free. Add the butter and continue mixing until fully blended, scraping down the bowl as necessary. Pour in both the granulated and brown sugar, then beat on medium-high speed for approximately 2 minutes, until the mixture becomes light and creamy. Crack in the egg and add the vanilla extract, then mix on high speed until everything is well incorporated. Scrape the bowl’s sides and bottom, then give it one final mix.
Gradually add the dry ingredients to the wet mixture, keeping the mixer on low speed to prevent overmixing. Once combined, stir in the white chocolate chips, ensuring they are evenly dispersed. Next, add the chopped Oreos and either mix on low speed or gently fold them in using a silicone spatula or wooden spoon—this dough will be thick and slightly heavy. Cover the dough and refrigerate for at least 2 hours, or up to 4 days. If chilling for longer than a few hours, allow the dough to sit at room temperature for about 30 minutes before scooping, as it will firm up significantly.
Preheat your oven to 350°F (177°C) and line baking sheets with parchment paper or silicone baking mats. Set aside.
Scoop out heaping 1.5-tablespoon portions of cookie dough (a medium-sized cookie scoop works well) and arrange them about 3 inches apart on the prepared baking sheets. Bake for 12 to 13 minutes, or until the edges appear lightly golden while the centers remain soft.
Once baked, remove the cookies from the oven and let them rest on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely. While still warm, press a few extra white chocolate chips or Oreo pieces on top for an enhanced presentation.
Store cookies in an airtight container at room temperature for up to 1 week, keeping them soft and fresh.