Preheat oven to 350 degrees. Line a 9″x 9″ inch pan with parchment paper. Set aside.
In a small saucepan, heat butter and chocolate until melted. Stir until smooth. Set aside to cool.
In a large bowl, whisk together 2 eggs, sugar, vanilla and red food coloring. Slowly add in the chocolate mixture and mix well. Batter should be red. If you would like a darker red color, add another 1/2 tsp. red food coloring. Add flour and salt and stir until combined.
Pour into prepared pan into an even layer.
Beat together cream cheese, sugar, 1 egg and vanilla until smooth. Drop onto brownie mixture and swirl with a knife.
Bake for 35-40 minutes until brownies and cheesecake are set.