In large heatproof bowl, over saucepan of hot (not boiling) water, melt chocolate with butter. Let cool slightly. Whisk in sugar, eggs and vanilla. Stir in flour, baking powder and salt. Set aside.
Cheesecake: In bowl, eat cream cheese with sugar until smooth, beat in egg. Dissolve coffee granules in vanilla and add to cheese mixture. Stir in flour.
Remove 1/2 cup of the chocolate batter to small bowl and spread remaining batter in parchment paper lined 8 inch square metal cake pan. Spread cheesecake batter over top. By spoonfuls, drop reserved chocolate batter over top. Run knife through batter to make decorative swirls.
Bake in 350 degree oven until tester inserted in center comes out with a few moist crumbs clinging, around 30-35 minutes. DO NOT OVER BAKE.
Let cool in pan on rack. Refrigerate for 4 hours. (make ahead: wrap and refrigerate for up to 2 days). Cut into squares.