Preheat the oven to 350°F. Line a 9x9-inch square baking dish with parchment or spray with cooking spray, and set aside.
In a large bowl or the bowl of a stand mixer, mix the butter and sugar until combined. Add the eggs, vanilla, food coloring, and vinegar, and mix to combine. Add the cocoa powder, flour, baking soda, and salt, and mix until combined. Spread the batter in the prepared pan, reserving ½ cup of batter.
In a medium bowl, beat the cream cheese with the sugar until combined. Add the egg and vanilla, and mix until smooth. Spread the cheesecake mixture over the brownie batter.
Scoop the remaining brownie batter into a ziplock bag and cut a small piece off the corner of the bag. Pipe the brownie batter in lines across the top of the cheesecake layer. Drag a toothpick through the lines to create a swirl pattern.
Bake for 30-35 minutes, or until a toothpick inserted into the brownies comes out clean. Let cool before serving.