Preheat oven to 350 °F (175 °C). Line a 9x13-inch baking pan with parchment or grease it lightly.
In a large bowl, whisk melted butter and sugar until combined. Add eggs one at a time, mixing well after each. Stir in vanilla.
Sift in flour, cocoa powder, and salt. Stir until just combined to form brownie batter.
In another bowl, beat softened cream cheese with sugar until smooth. Add eggs one at a time, then vanilla extract, mixing until creamy.
Pour about two-thirds of the brownie batter into the pan, spreading evenly.
Dollop the cheesecake mixture over the brownie batter layer.
Add remaining brownie batter in spoonfuls over the cheesecake layer.
Drizzle caramel sauce on top and use a knife or skewer to swirl it for a marbled effect.
Bake for 35–45 minutes until edges are set and center is slightly jiggly but not wet.
Cool completely, then refrigerate at least 2 hours before slicing. Optionally drizzle extra caramel before serving.