Pre-heat the oven to 350 degrees. In a small pan on the stove top melt butter and dark chocolate sitting until smooth. Remove from heat and allow it to cool.
In a large bowl mix together sugar, eggs, vanilla extract. Pour butter/chocolate mixture into sugar mixture and mix well. Stir in flour and cocoa. Mix until well combined. Grease an 8 x 8 baking dish and pour the mixture into the dish.
To prepare cheesecake topping – soften cream cheese in the microwave if necessary. In a bowl beat cream cheese, sugar, egg, and vanilla extract until smooth.
Slowly spoon cheesecake mixture over the chocolate mixture in the baking dish and gently swirl with a butter knife.
Bake for 30-40 minutes or until the brownies is set. Remove from oven and allow brownies to cool.