Preheat the oven to 350°F (175°C). Line a 9×13-inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
In a large bowl, whisk together the melted butter and granulated sugar until smooth.
Add the eggs, one at a time, mixing well after each addition. Stir in the vanilla extract.
Add the cocoa powder, all-purpose flour, and salt. Mix just until combined; do not overmix.
Reserve 1 cup of the brownie batter for the swirl. Spread the remaining batter evenly into the prepared baking pan.
In a separate bowl, beat the softened cream cheese until smooth and creamy.
Add the sugar, egg, and vanilla extract to the cream cheese and mix until smooth and lump-free.
Spread the cheesecake mixture evenly over the brownie batter.
Spoon the reserved brownie batter over the cheesecake layer in small dollops.
Use a butter knife or toothpick to gently swirl the brownie batter through the cheesecake layer to create a marbled pattern.
Bake for 38–45 minutes, or until the edges are set and the center has a slight jiggle. A toothpick inserted into the brownie portion should come out with a few moist crumbs.
Let the brownies cool in the pan for 1 hour at room temperature.
Refrigerate for at least 2 hours before slicing for clean, neat squares.
Lift the brownies from the pan using the parchment paper, cut into 16 squares, and serve chilled or at room temperature.