Preheat oven to 350F. Line an 8- or 9-inch square baking pan with aluminum foil and lightly grease.
In a small, heatproof bowl, melt butter and chocolate together.
Stir with a fork until very smooth. Set aside to cool for a few minutes.
In a large bowl, whisk together sugar, eggs, vanilla extract and red
food coloring. Add in the chocolate mixture and stir until smooth.
Batter should be red. If a brighter red is desired, add an additional
1/2 tsp food coloring. Add flour and salt into the bowl and stir until everything is just combined and no streaks of dry ingredients remain.
Pour into prepared pan and spread into an even layer.
Prepare cheesecake mixture. In a medium bowl, beat cream cheese,
sugar, egg and vanilla extract until smooth. Drop in dollops onto
prepared brownie batter. Gently swirl two batters with a butter knife.
Bake for 35-40 minutes, until brownies and cheesecake are set. A
knife inserted into the cheesecake mixture should come out clean and
the edges will be lightly browned.
Cool in the pan completely before slicing and serving, either at room temperature or chilled.
*Brownies can be refrigerated, covered, for several days*