Preheat oven to 350°F (170°C). Butter 9x13 inch (25x40 cm) baking pan.

For the Cheesecake Filling: beat cream cheese, sugar, vanilla and egg for one minute until creamy. Set aside.

For the Brownie Batter: in a large mixing bowl, beat the butter, sugar and cocoa powder until fluffy. In a different bowl, lightly beat the eggs then add the vanilla, red food coloring and vinegar and whisk until the food coloring is completely dissolved. You can add as much food coloring you wish to reach the desired intensity of red. Add the red egg mixture to the butter-cocoa mixture and blend well. Add the flour and salt and mix until combined.

Spread ¾ of the brownie batter in the baking pan. Pour all of the cheesecake filling mixture over the brownie batter and spread evenly. Drop tablespoons of the remaining brownie batter on top of the cheesecake layer. Pull a knife through the pan in wide curves a couple of times to create swirls.*

Bake brownies for 30-35 minutes. Cool completely in pan on a wire rack. Cover and chill for at least two hours before cutting into brownies. Brownies keep for up to 4 days in the refrigerator.