Preheat the oven to 350 degrees F. Prepare a 9x9 baking pan by lining it with parchment paper, set aside.
In a medium size bowl, beat the butter and cream cheese together until smooth using a hand or stand mixer.
Add in the sugars and cream together with the butter mixture.
Pour in the vanilla extract and add the eggs. Mix until smooth and creamy.
Add the flour, baking powder, and salt. Mix on low speed until batter comes together. It will be sticky.
Fold in the white chocolate chips and 1 cup of the chopped Oreos.
Using a rubber spatula, scoop the batter into the prepared baking pan. The batter will be sticky. Spread it out into an even layer.
Top with the remaining chopped Oreos, gently pressing into the batter.
Bake for 26-28 minutes until the edges are just starting to turn golden.
Remove from the oven and let the bars cool in the baking pan for 30 minutes, then remove from the pan by pulling up the parchment paper and set on a wire rack to continue cooling another 2-3 hours before cutting.