Preheat oven to 325°. Line baking sheets with silicone mats or parchment paper.
In a medium bowl, add flour, cornstarch, baking powder, and salt. Whisk well to combine. Set aside.
Make sure your butter is cold, cut into cubes. Add to a large mixing bowl with granulated sugar and packed brown sugar. Cream with hand or stand mixer on high for about 3 minutes. The mixture will look very clumpy at first, continue to mix until fully combined, but you will still have some lumps.
Add the eggs and vanilla extract to the butter mixture. Mix on medium speed for 1-2 minutes until well combined. It will still have small clumps, but be more cohesive.
Add the flour mixture ¼-½ cup at a time. Mix well in between each addition. Once the dough is fully formed, you can stop beating.
Add Oreos to a separate bowl and crush with your hands into large chunks. Add Oreo pieces and white and chocolate chips to the dough. Stir in by hand until evenly incorporated.
Using a large cookie scoop or a small ice cream scoop, drop cookie dough on prepared baking sheets. Cookies should be 75g or about a heaping ¼ cup. Make sure to space them out at least 3".
Bake for 15-17 minutes. Remove from oven when bottom edges start to turn slightly golden brown. Let cookies sit on the sheet for 5-10 minutes before removing and let them cool on wire rack.