1.Preheat oven to 350F. Butter the bottom and sides of a 8 inch metal baking pan. Put a long piece of parchment paper in the bottom of the pan, letting the parchment extend up two sides of the pan and overhang slightly on both ends. (This will make it easy to remove the bars from the pan after they have baked.) Butter the parchment.
2.In a small, heatproof bowl, melt butter and chocolate together. Stir until combined and very smooth. Set aside to cool for a few minutes.
3.In a large bowl, whisk together sugar, eggs, vanilla extract and red food coloring. Add chocolate mixture and stir until smooth. Add flour and salt and stir until just combined and no streaks of dry ingredients remain.
4.Pour into prepared pan and spread into an even layer.
5.To prepare cheesecake mixture, beat cream cheese, sugar, egg and vanilla extract in a medium bowl until smooth. Distribute the cheesecake mixture in 8 dollops over batter in the pan. Swirl in with a knife or spatula.