Preheat oven to 350°F. Line an 8×8-inch baking pan with parchment paper leaving a couple inches of overhang for easy lifting. Use cooking spray to grease the sides not covered with paper. Set aside.

Red Velvet Brownies: In a large bowl, stir together the melted butter, sugar, cocoa powder, salt, red food coloring, vanilla, and vinegar. Combine well.

Stir in the eggs one at a time, incorporating well with each addition. Add the flour and stir until just combined. Set batter aside.

Cheesecake: In another large bowl, beat together the cream cheese, sugar, and vanilla with an electric hand mixer. Add the egg and blend until smooth. Set aside.

Assembling: Reserve 1/2 cup of red brownie batter for topping. Pour the remaining red velvet batter into the prepared pan.

Pour the cheesecake batter evenly over the red velvet batter.

Dollop the reserved 1/2 cup of red velvet brownie batter over the cream cheese layer. Use a butter knife or toothpick to swirl the cheesecake together with the dollops of red velvet batter. TIP: Don't over-do the swirling. Less is more. It might be helpful to make "figure 8" swirls.

Bake at 350°F for 30 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs of brownie batter or thick baked cheesecake stuck to it. If it still looks wet, bake a few minutes more.

Cool completely before lifting the parchment out of the pan to cut the brownies into squares.