Preheat oven to 350 F.
Melt butter and chocolate. An easy way to do this is by using a metal bowl over a pot of boiling water double boiler style.
Once melted remove from heat and whisk in sugar, eggs, and vanilla.
Whisk in flour until well combined.
Pour into an 8 or 9 inch baking pan.
Whisk cream cheese, sugar, egg yolk, and vanilla until well combined.
Add spoonfuls of the mixture to the pan on top of the brownie mixture.
Marble by swirling with a knife.
Top with mini chocolate chips.
Bake for 30-40 minutes until center is set.