Preheat your oven to 350 degrees Fahrenheit.
Line an 8x8 inch baking dish with parchment, and set aside.
In a medium mixing bowl, mix the melted butter and sugar together. Add the eggs, white vinegar, vanilla, and food coloring, and mix well to combine.
In a medium bowl, whisk together the flour, cocoa powder, and salt. Add the dry ingredients to the wet, mixing until just combined.
In a separate mixing bowl, beat the cream cheese until smooth. Add in the sugar, egg, and vanilla, and mix to combine.
Add 2/3 of the red velvet batter to your prepared baking dish, and smooth out evenly. Pour the cheesecake mixture over top. Drop the remaining 1/3 batter over top of the cheesecake in large spoonfuls. Use a butter knife to swirl the red velvet and cheesecake together. Bake for 30-35 minutes, until the center cheesecake part is no longer jiggly.
Allow the brownies to cool, and enjoy.