Preheat the oven to 375°F (190°C)and line a baking tray with parchment paper.
In a bowl, beat the room temperature butter until light and fluffy using an electric whisk or stand mixer fitted with a paddle attachment.
Add the cane or castor sugar & light brown sugar and beat until creamy. Scrape down the sides and mix in the room temperature yogurt & vanilla extract until combined.
Add the flour, cornstarch, baking powder, baking soda, and salt, mixing just until combined. Fold in the chopped Oreo and chocolate chips, reserving a few to press on top before baking.
Scoop the dough into 5 balls (about 120-130g each for large Oreo cookies or 65g for smaller ones).
Place cookie dough on the prepared tray, leaving space between each cookie, and press extra chocolate chips and Oreo chunks on top if desired.
Bake for about 12 minutes for large cookies, or 8 minutes for smaller cookies until the edges are set while the centers remain soft. For perfectly round cookies, gently reshape them with a cookie cutter or a bowl right after baking while still warm.
Sprinkle with flaky sea salt if desired and let cool on the tray for 30 minutes before transferring to a wire rack.
Store the cookies in an airtight container at room temperature for up to three days. For a freshly baked feel, warm a cookie in the microwave for 10 to 15 seconds to bring back the gooey center. The dough can also be frozen and baked fresh when needed.