Preheat the oven to 350°F. Line an 8- or 9-inch square pan with parchment paper, leaving overhang on two sides for easy removal. Lightly coat with cooking spray.
Make the brownie batter: In a large bowl, whisk together melted butter, sugar, and cocoa powder until smooth. Add eggs and vanilla and whisk again. Stir in flour and salt until fully combined. Set aside.
Spread ¾ of the brownie batter evenly into the prepared pan. Reserve the remaining batter for swirling.
Prepare the cheesecake layer: In a medium bowl, beat the softened cream cheese and sugar for 2–3 minutes until smooth and creamy. Add the egg and vanilla extract and beat until fully incorporated.
Pour the cheesecake mixture evenly over the brownie layer.
Stir 1 tablespoon of very hot water into the reserved brownie batter until smooth and pourable. Dollop this batter over the cheesecake layer.
Use a knife or skewer to gently swirl the brownie batter into the cheesecake layer.
Scatter raspberries evenly over the top.
Bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean or with just a few moist crumbs.
Cool completely in the pan. Lift out using the parchment, slice into squares, and serve.