Preheat oven to 350 degrees. Line a 9x9 inch baking pan with parchment paper or spray well with non-stick spray.
In a saucepan melt butter and chocolate together over medium-low heat. Once melted, remove from heat and mix in sugar, buttermilk and vanilla until well blended. Whisk in eggs until smooth. Mix in flour and baking powder until just combined.
Pour into prepared baking pan, reserving 1/3 cup of batter.
In a bowl beat cream cheese, sugar, egg yolk, and vanilla until smooth and creamy. Drop dollops of cream cheese mixture over the top of the batter. Using a knife, swirl the cream cheese mixture into the batter. Top with the reserved batter and swirl again.
Bake for 25-30 minutes until a toothpick comes out clean.
Remove from oven and let cool completely before slicing to serve.