Preheat oven to 350 degrees. Coat a 9 x 9 inch baking pan with cooking spray and line with parchment paper.
For the brownie layer, whisk together first six dry ingredients, through salt, in a large mixing bowl. Set aside.
Combine the milk and chocolate chips in a microwave safe dish. Cook on high, stopping to stir after 30 second increments, until the chocolate is melted (about 1 minute). Whisk together the melted butter, eggs, and vanilla.
Pour the chocolate mixture into the dry ingredients and stir to combine. Fold in the white chocolate chips and pour the batter into the prepared pan. Press 16 of the Oreo cookies into the brownie mixture, spacing out evenly around the pan.
For the cheesecake layer, in a medium bowl combine the cream cheese, sugar, vanilla, and egg, and beat with a handheld mixer until smooth. Pour the cheesecake mixture on top of the Oreos in the baking pan, trying to leave a 1 inch border from the edge of the pan. Sprinkle on the chopped Oreos.
Bake for 35-40 minutes, until brownie edges start to pull away from pan. Cool on a wire rack for at least 2 hours. Cover and refrigerate for another 2 hours before cutting and serving.
Notes
Make Oreo Cheesecake Brownie Bars ahead of time and refrigerate for up to a week. Can also be frozen: store in an airtight container and freeze for up to a month.