Preheat your oven to 350°F (175°C). Grease an 8x8-inch baking pan lightly with butter or line it with parchment paper.

In a medium bowl, whisk together the melted unsalted butter and granulated sugar until smooth and glossy, about 2-3 minutes. Add the large eggs one at a time, mixing thoroughly after each addition.

Sift the unsweetened cocoa powder and all-purpose flour into the brownie mixture. Gently fold with a spatula until just combined; avoid overmixing.

In a separate bowl, beat the cream cheese, powdered sugar, and vanilla extract until smooth and free of lumps, about 2-3 minutes.

Pour half of the brownie batter into the prepared pan, spread evenly, dollop the cheesecake mixture on top, then add the remaining brownie batter. Swirl together with a knife or toothpick.

Bake in the preheated oven for 30-35 minutes. Check doneness with a toothpick; it should come out with a few moist crumbs.

Remove from the oven and let cool completely in the pan on a wire rack, about 30 minutes.