Preheat oven to 350°F (175°C). Grease a 9x9 inch baking pan.
In a mixing bowl, combine melted butter, sugar, vanilla extract, and red food coloring. Add eggs one at a time, mixing well after each addition.
In another bowl, whisk together flour, cocoa powder, and salt. Gradually add to the wet ingredients, mixing until just combined.
Pour the batter into the prepared baking pan, reserving a small amount for the top.
In a separate bowl, beat the cream cheese, sugar, egg, and vanilla extract until smooth. Drop spoonfuls of the cream cheese mixture over the brownie batter. Use a knife to swirl the cream cheese mixture into the batter.
Dollop the reserved brownie batter over the top and swirl again.
Bake for 30 minutes or until a toothpick inserted into the center comes out clean. Allow to cool before cutting into squares.