Preheat oven to 350°F (175°C).
In a large bowl, whisk together the melted butter, granulated sugar, and brown sugar until well combined. Add the eggs one at a time, whisking well after each addition. Stir in the vanilla extract and red food coloring until everything is evenly colored.
In a separate bowl, whisk together the cocoa powder, flour, baking soda, and salt. Gradually add the dry ingredients to the wet ingredients, mixing until just combined.
In a medium bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the egg and vanilla extract, and beat until just combined.
Pour the brownie batter into the prepared pan. Drop spoonfuls of the cheesecake batter over the brownie batter. Use a knife or toothpick to swirl the cheesecake into the brownie batter.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out with moist crumbs attached.
Let the brownies cool completely in the pan before cutting into squares.
