Preheat oven to 350°F (175°C) and grease or line an 8x8-inch baking pan with parchment paper.

In a large mixing bowl, whisk together the melted unsalted butter and granulated sugar until smooth. Add eggs one at a time, blending well after each addition.

Sift cocoa powder and flour into the bowl, gently stir until just combined.

In a separate bowl, beat together cream cheese, powdered sugar, and vanilla until smooth.

Pour half of the brownie batter into the prepared pan, dollop cheesecake mixture on top, pour remaining brownie batter, and swirl together gently.

Bake for 30-35 minutes, check for doneness with a toothpick.

Let brownies cool completely before slicing into squares.