Preheat your oven to 350°F (175°C) and prepare a 9x13-inch baking dish by greasing it or lining it with parchment paper.
In a large mixing bowl, whisk together the melted butter and granulated sugar until well incorporated. Add the eggs one by one, whisking thoroughly after each addition, then stir in the vanilla extract.
In a separate bowl, sift together the flour, cocoa powder, and salt. Gradually incorporate the dry mixture into the wet ingredients, mixing gently until just combined. Fold in the crushed Oreo cookies, reserving some for topping.
In another mixing bowl, beat the softened cream cheese with the powdered sugar until smooth. Add the egg and vanilla extract, mixing until well blended.
Spread half of the brownie batter into the prepared baking dish. Spoon the cheesecake mixture over it, smoothing it out. Dollop the remaining brownie batter on top and use a knife to swirl the batters together.
Bake in the preheated oven for 30-35 minutes. Check for doneness with a toothpick; it should come out mostly clean with a few moist brownie crumbs.
Allow the brownies to cool in the pan for at least 15 minutes before slicing. Sprinkle with reserved crushed Oreo cookies before serving.
Notes
Serve with melted chocolate or caramel sauce and a scoop of vanilla ice cream for an extra indulgence.