Line two cookie sheets with silicone baking mats or parchment paper.

In a large bowl, beat together the butter and sugars until fluffy and well-combined.

Beat in eggs one at a time, scraping down the sides as needed.

Stir in vanilla extract until incorporated.

In a separate medium bowl, whisk together the flour, cornstarch, baking soda, and salt.

Stir in flour mixture until just incorporated.

Gently fold in chocolate disks and Oreos until just combined.

Cover, and refrigerate dough at least 3 hours (up to 24 hours). The cookies will hold their shape better if you refrigerate the dough for 8-24 hours.

Toward the end of the chilling time, preheat oven to 350 F.

Drop scoops of dough onto prepared cookie sheets using a medium cookie scoop (1 ½ tablespoons).

Bake for 8-9 minutes. You want the edges to be just barely golden brown.

Remove from oven, and let cool for 5-10 minutes on the cookie sheet.

Transfer to wire rack to finish cooling.