Start by preheating your oven to 350°F and lining your baking sheets with parchment paper; set them aside. In a medium-sized mixing bowl, beat together the softened butter, brown sugar, granulated sugar, egg, and vanilla extract until the mixture is smooth and creamy. Next, sprinkle the flour, cornstarch, and baking soda over the wet mixture and stir until a soft dough forms. Gently fold in the chocolate chips. Using a large cookie scoop (about ¼ cup of dough), portion out the dough and flatten it in your hand. Place an Oreo in the center, then top with a bit more dough and seal the edges completely by pinching them together. Arrange the assembled cookies on your prepared baking sheets, leaving space between each. Bake for 15 to 18 minutes, or until the edges are set. Allow the cookies to cool on the baking sheets until they are firm enough to transfer.