1. Heat oven to 350°F. Grease 9-inch square baking pan.
2. Stir together butter, sugar and vanilla in bowl. Add eggs; beat well with spoon. Stir together flour, cocoa, baking powder and salt; gradually add to egg mixture, beating until well blended. Spread batter evenly in prepared pan.
3. Stir together the cream cheese and 1/3 cup sugar with a spoon until smooth and well blended. Gently stir in in the chopped Oreo cookies.
4. Using a spoon, spoon the cream cheese/Oreo mixture in nine evenly-spaced dollops on top of the brownie batter. Using a dull knife or icing spatula, gently swirl the cream cheese mixture with the brownie batter. Remember, less is more here.
5. Bake 30 to 35 minutes or until brownies begin to pull away from sides of pan and the batter in the center of the pan feels just set. Cool completely in pan on wire rack.