Microwave chocolate and butter in bowl at 50 percent power until melted.
Whisk sugar, eggs, and vanilla together.
Add the melted chocolate mixture and combine.
Add flour, baking powder and salt to combine.
Transfer 1/2 cup batter to a different bowl for later.
Spread rest of the batter into pan.
Spread cream cheese filling evenly over batter.
Microwave the bowl of reserved batter until warm and pourable, 10 to 20 seconds.
Dollop this over the cream cheese and use a knife to swirl the 2 together.
Bake 35 to 40 minutes.
Cool one hour.
Chill if serving them cold!