Preheat oven to 350°F and line a 9x13-inch pan with parchment paper.
In a large bowl, whisk together melted butter, sugar, eggs, vanilla, cocoa powder, flour, and salt until smooth.
Pour most of the brownie batter into the pan, reserving about 1/2 cup for topping.
In another bowl, beat cream cheese, sugar, eggs, and vanilla until smooth and creamy.
Spread the cheesecake mixture evenly over the brownie batter in the pan.
Dollop the reserved brownie batter on top and swirl with a knife for a marbled effect.
Bake for 45-50 minutes, until the center is set but still slightly jiggly.
Cool completely, then refrigerate for at least 4 hours before slicing.