Special equipment: 8 by 8-inch baking pan
Preheat the oven to 350 degrees F.
Butter an 8 by 8-inch baking pan, and set aside.
Brownie layer: In a saucepan on medium heat melt the butter. Remove the butter to a large bowl and add the sugar, vanilla, cocoa powder, salt, food coloring, and vinegar, in that order, mixing between additions. Whisk the eggs in a small bowl and stir it into the cocoa mix. Fold in the flour until lightly combined. Stir in the walnuts and pour the batter into the prepared baking pan, saving 1/4 cup of the batter for the top.
Cream cheese layer: Blend together the cream cheese, sugar, egg, and vanilla in a medium bowl. Gently spread the cream cheese layer on top of the brownie batter in the pan. Dollop the remaining brownie batter over the cream cheese layer. Using a skewer or the tip of a knife, drag the tip through the cream cheese mixture to create a swirl pattern. Bake the brownies for 30 minutes. Remove to a cooling rack and allow them to cool completely before cutting.