Preheat oven to 180 degrees. Grease a brownie pan.
Melt butter and chocolate over low flame. Remove off heat.
Add the sugar and vanilla extract and whisk in well till sugar is well combined.
Add in the eggs one at a time and beat with each addition. Add in the dry ingredients and fold till all moist.
In another bowl, whisk all ingredients for the cheese layer till homogeneous.
Pour 3/4 of the batter into the pan and spread. Spread the cheese layer on the top. Drop the remaining brownie batter and using a fork, make swirls.
Bake for 30 minutes. Allow to cool completely before slicing in serving.