Preheat oven to 325°F. Spray a 10-inch bundt pan with nonstick cooking spray. Set aside.
In the bowl of a stand mixer fitted with a paddle attachment, cream together the softened butter, cream cheese, and granulated sugar on medium speed until light and fluffy, about 3-4 minutes.
Add the eggs one at a time, beating well after each addition. Mix in the vanilla extract. Remove bowl from the stand mixer.
In a separate bowl, whisk together the cake flour, cocoa powder, baking powder, and kosher salt.
Add the dry ingredients to the butter mixture. Stir until just combined.
Gently fold in the chopped Oreos, being careful not to overmix.
Pour the batter into the prepared Bundt pan and smooth the top with a spatula. Bake for 90-95 minutes, or until a toothpick inserted into the center comes out with a few crumbs but no wet batter.
Allow the cake to cool in the pan for about 10-15 minutes before inverting it onto a wire rack to cool completely.