In the bowl of a stand mixer combine the melted butter, granulated sugar, light brown sugar and vanilla extract. Mix on medium for 1 minute. Add in both eggs and mix on low until incorporated. Add in the flour, corn starch, cocoa powder, baking soda and salt and mix on low until everything is combined.
Line a baking sheet with parchment paper (you can also use wax paper, but do not bake with the wax paper) Use a medium sized cookie dough scoop to scoop 20 even cookies and place on the prepared baking sheet. One by one flatten the dough and place 1 Oreo in the center. Fold the up around the completely cover the Oreo and place back on the baking sheet. Refrigerate for 30 minutes to chill the cookie dough. This will help to enhance the flavor and prevent spreading. Preheat the oven to 350°
Once the cookie dough has chilled, space each about 2 inches apart on a cookie sheet lined with parchment paper and bake for 9-10 minutes, or until the edges are just set. Let the cookies cool on the baking sheet for 3 minutes before transferring to a cookie rack to cool completely.
Once cooled completely, melt white chocolate in a heatproof bowl in the microwave. Heat for 20 seconds at a time, stirring in between, until smooth. Drizzle over cooled cookies and let the chocolate set before serving, about 5 minutes.