Preheat the oven to 350 degrees Fahrenheit
Prepare the brownie pan by greasing with butter or non stick spray and laying in 2 pieces of parchment paper to cover the bottom and sides leaving an overhang to help lift the brownies out. Grease the parchment paper as well.
Melt the butter, cocoa powder, chocolate, vanilla, coffee, and salt together in a heat safe bowl over a pan of simmering water, stirring occasionally.
Once that is melted and smooth set it aside to cool slightly and mix the cheesecake filling.
Mix the cheesecake filling ingredients in bowl with either a hand mixer or whisk until well combined and smooth.
Set aside and go back to the brownie batter.
Stir the granulated and brown sugars into the melted chocolate mixture.
Add in the beaten eggs and mix well to combine.
Add in the flour and fold in until just combined.
Pour the brownie batter into the prepared pan.
Drop the cheesecake filling in dollops on top of the brownie batter and swirl it in the a skewer, chopstick, or knife.
Bake the brownies at 350 for 35-45 minuted or until a toothpick inserted in the center comes out clean or with a few moist crumbs.
Cool the brownies on a rack on the counter for 20-30 minutes and then cool completely in the refrigerator.
Once cooled lift the brownies out of the pan with the parchment overhang and cut into desired size squares.