Line 2 cookie sheets with silicone baking mats or parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment (or with an electric mixer), beat together the butter and sugars until fluffy well-combined, about 3-4 minutes.
Beat in eggs one at a time, scraping down the sides as needed.
Stir in vanilla until incorporated.
In a separate medium bowl, whisk together the flour, cocoa powder, cornstarch, baking soda, and salt.
Stir in flour mixture until just incorporated.
Add the chocolate chunks and chopped Oreos; stir until just combined.
Cover, and refrigerate dough at least 3 hours (up to 24 hours). The longer you refrigerate it, the more the dough will hold its shape as it bakes. Ideally, plan for 8-24 hours. The dough will stay good (covered) in the fridge for up to 3 days.
Toward the end of the chilling time, preheat oven to 350 F.
Using a medium ( 1 ½- tablespoon) cookie scoop, drop scoops of dough about 2 inches apart on prepared cookie sheet.
Bake for 8-9 minutes (don’t bake them any longer than 9 minutes). They may look soft and almost underdone, but that’s ok.
Remove from oven, and let cool for 5-10 minutes on the cookie sheet.