Prep two large aluminum cookie sheets with parchment paper and set aside.
Preheat oven to 410 degrees (yep, that's right!)
In a stand mixer fitted with a paddle attachment, whip up the butter for 1 minute until it's light and fluffy, then add in the sugars to cream together with the butter for 3 minutes on high speed.
Scrape down the sides of the bowl and then add in the eggs, vanilla, lemon zest and flavoring. Mix again until combined.
Add in the flour, cornstarch, baking soda, and salt and slowly mix together on the very lowest mixer speed until just combined (don't overmix!)
Reserve 1/8 cup of the white chocolate chips and shortbread/Oreos, then mix in the rest on the lowest speed. Split the dough into 8 balls (baseball-sized) and place 4 on each cookie sheet. Hand-press on the chocolate and shortbread/Oreos.
Bake for 7-9 minutes. They should be slightly golden on the outside, slightly mounded in the middle, and thick/tall, and gooey in the center. Let them cool on the pan for 1 minute, then carefully transfer the cookies to a cooling rack to finish cooling. Enjoy!