In a medium-sized bowl, whisk together the flour, cornstarch, baking soda, and salt. Set aside.
In a separate large bowl, vigorously whisk together the melted butter, brown sugar, and granulated sugar until completely combined.
Add the egg and vanilla extract and whisk until combined. Add the dry ingredients to the wet ingredients and fold until almost combined but with a few streaks of flour remaining.
Add both types of chocolate chips and fold until thoroughly incorporated and the flour is fully mixed in.
Cover the bowl tightly and chill the cookie dough for at least three hours.
Once the dough is done chilling, preheat your oven to 350F and line a baking sheet with parchment paper.
Scoop a ball of dough measuring about 1 ½ tablespoons (~30 grams), and flatten it in between your palms. Place an Oreo on top of the flattened cookie dough.
Scoop a second ball of dough measuring about 2 tablespoons (~40 grams), flatten, and place that on top of the Oreo. Pinch the top and bottom pieces of cookie dough together until sealed. Repeat with the rest of the dough.
Place on the prepared baking sheet, spacing the cookies about 3 inches apart. Bake for 10-12 minutes until the edges are set and golden.
Let cool on the pan for 5 minutes, then transfer to a cooling rack to cool completely. Top with more chocolate chips if desired.
Store in an airtight container at room temperature.