Preheat your oven to 350 degrees Fahrenheit.
Grease an 11 x 7 x 2-inch baking pan.
In a small bowl, beat together the cream cheese, ¼ cup of sugar, 1 egg, and ½ teaspoon of vanilla extract until smooth.
In a large bowl, combine the melted butter, ½ cup of white sugar, packed brown sugar, and baking cocoa powder. Stir until thoroughly combined.
Add 2 eggs, one at a time, beating well after each addition.
Combine the flour and baking powder in a separate bowl, then stir it into the cocoa mixture.
Add the remaining vanilla extract and crushed Oreo cookies to the mixture, stirring gently to incorporate.
Pour the brownie batter into the greased baking pan.
Spoon the cream cheese mixture in dollops over the brownie batter.
Use a knife to swirl the cream cheese mixture into the brownie batter.
Bake at 350 degrees for 25 to 30 minutes.
Once baked, allow the brownies to cool completely in the pan before cutting.