Preheat your oven to 350 degrees.
In a large bowl using an electric mixer or stand mixer, beat together the 1 cup of butter & both white and brown sugars. Beat in the eggs one at a time until smooth. Stir in the food coloring & half the vanilla extract. Gently fold in the flour & cocoa, being careful not to over mix. I can’t stress that enough – don’t over mix! The batter will be very thick.
Spray a 9×13 inch baker with non-stick cooking spray or Baker’s Secret. Pour in the brownie batter, scraping the sides of the bowl to get it all out.
In a large bowl, beat together the cream cheese and 2 tablespoons of butter until smooth. Mix in the flour, vanilla, sweetened condensed milk, & the egg until well combined. Spread the cream cheese mixture over the brownie batter. Bake at 350 degrees for 45 minutes.