Preheat your oven to 350°F (180°C). Line an 8x8-inch baking pan with parchment paper, leaving some overhang for easy removal later. Grease the unlined sides to prevent sticking.

In a mixing bowl, combine melted unsalted butter, granulated sugar, cocoa powder, and salt. Stir in red food coloring, vanilla extract, and distilled white vinegar until well blended. Add the eggs one at a time, mixing in between, then gently fold in the all-purpose flour until just combined.

In another bowl, beat the softened cream cheese, granulated sugar, and vanilla extract together until smooth and creamy. Add in the large egg and blend until fully incorporated.

Pour half of the brownie batter into the prepared pan, smoothing it out evenly. Dollop the cheesecake batter on top, carefully spreading it without disrupting the brownie layer. Spoon the remaining brownie batter randomly over the cheesecake layer, then use a knife to gently swirl the two batters together.

Place the pan in the preheated oven and bake for 30 minutes, or until a toothpick inserted into the center comes out with moist crumbs.

Once baked, remove the pan from the oven and let it cool completely in the pan. Once cool, lift the brownies out using the parchment overhang, and place on a cutting board. Cut into squares and enjoy this delightful dessert.