Preheat oven to 350 degrees Fahrenheit. Line the bottom of a 9- x 13-inch cake pan with Gefen Parchment Paper or foil.
In a medium saucepan, melt the butter and chocolate over low heat, stirring until smooth. Remove from heat and mix in sugar and then eggs, stirring vigorously with each addition. Mix in flour, cocoa, salt, and vanilla extract, stirring just until smooth.
To make the cheesecake mixture, place all the ingredients in a medium bowl and mix until combined (I like to use an immersion blender.)
Spoon the remaining brownie mixture over the top of the cheesecake mixture in 8 dollops of approximately 1 tablespoonful each.
Take a knife or spatula and run it through the dollops, creating a swirl design on top. Bake for 40 minutes, just until set. Cool completely, then cut into squares.
Pour a bit more than half the brownie mixture into the bottom of the pan and spread evenly. Pour the cheese mixture gently on top of the brownie layer and smooth with a spoon.