Prepare the Red Velvet Brownie Batter. In a large mixing bowl, combine the red velvet cake mix, eggs, butter, and red food coloring (if using) until smooth.
Make the Cheesecake Swirl. In another bowl, beat together the cream cheese, powdered sugar, and vanilla extract until creamy. Add the eggs one at a time, mixing well after each addition.
Layer and Swirl. Pour most of the red velvet brownie batter into a greased baking dish, reserving a small amount. Spoon the cheesecake mixture over the brownie batter. Drop spoonfuls of the reserved brownie batter and cheesecake mixture on top, then swirl gently with a knife to create a marbled effect.
Bake. Bake the brownies in a 350F preheated oven for 30 minutes or until set and a toothpick inserted into the center comes out with a few moist crumbs.
Cool and Serve. Allow the brownies to cool completely in the pan before slicing into squares and serving.