Preheat oven to 350 °F (175 °C). Prepare a 9x13-inch pan by lining with parchment paper or greasing it.
In a large bowl, whisk melted butter and sugar until combined. Add eggs one at a time, mixing well after each. Stir in vanilla extract.
Sift in flour, cocoa powder, and salt. Gently mix until just combined, being careful not to overmix.
In a separate bowl, beat softened cream cheese with sugar until smooth. Add eggs one at a time, then vanilla extract, mixing until creamy and well blended.
Pour about two-thirds of the brownie batter into the prepared pan and spread evenly.
Dollop the cheesecake mixture over the brownie batter layer.
Spoon the remaining brownie batter over the cheesecake mixture.
Drizzle caramel sauce over the top. Use a knife or skewer to swirl the caramel and brownie batter together for a marbled effect.
Bake for 35 to 45 minutes, until edges are set and center is slightly jiggly but not wet.
Allow to cool completely, then refrigerate at least 2 hours before slicing into bars.
Before serving, drizzle extra caramel sauce if desired.