Prepare the pan. Butter an 8 X 8-inch baking pan and set aside. Preheat the oven to 350 degrees Fahrenheit.
Mix the red velvet layer. Melt the butter in a small saucepan over medium heat. Transfer to a large bowl and mix between each addition of the sugar, vanilla, cocoa powder, salt, food coloring, and vinegar. Whisk the eggs in a small bowl and combine with the warm cocoa mix. Fold the flour into the chocolate batter and combine lightly. Add the walnuts and stir.
Mix the cream cheese layer. Blend the cream cheese, sugar, egg, and vanilla in a medium bowl.
Assemble the brownies. Pour the red velvet layer into the bottom of the prepared pan, saving ¼ cup batter for the top. Gently spread the cream cheese layer on top of the red velvet layer. Then randomly dollop the remaining red velvet batter over the cream cheese layer. Using a skewer or the sharp end of a knife, drag the tip through the cream cheese mixture to create a swirl pattern. Bake for 30 minutes. Transfer to a cooling rack and allow to cool completely before cutting into 2 X 2-inch brownies.