Preheat oven to 350 degrees. Spray an 8 inch square baking pan with cooking spray.
Line the pan with parchment paper, leaving excess on the sides to lift the bars out later. Spray the parchment with cooking spray.
Combine the flour, baking soda and salt in a bowl. In the bowl of a stand mixer fitted with the paddle attachment, cream the butter, brown sugar and granulated sugar on medium speed until light and fluffy, about 2 minutes.
Add the egg and vanilla extract, beating until incorporated. Scrape down the sides of the bowl with a spatula if needed.
With the mixer on low, add the dry ingredients, mixing just until combined. Be careful to not overmix.
Fold in half of the oreos, white chocolate and semisweet chocolate with a spatula.
Transfer the dough to the prepared pan and press into an even layer
Sprinkle the remaining oreos and chocolates over the top of the dough.
Bake for about 20-25 minutes, or until a toothpick inserted in the center comes out with just a few moist crumbs attached. I tested these with a metal pan, if you use a glass pan it may take 5 minutes longer to bake.
Transfer the pan to a wire rack and let the bars cool completely in the pan. Use the parchment overhang to lift the bars out and cut into squares for serving.