Preheat oven to 350F. Line an 8- or 9-inch square baking pan with aluminum foil and lightly grease. 9" Pan gives best results
In a small, heatproof bowl, melt butter and chocolate together in the microwave. Stir with a fork until very smooth. Set aside to cool for a few minutes.
In a large bowl, whisk together 1 cup sugar, 2 eggs, 2 tsp vanilla extract, vinegar, and red food coloring. Add in the chocolate mixture and stir until smooth.
The batter should be red. Add flour and salt to 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. Reserve a few teaspoons to go on top of the cheesecake batter.
Prepare cheesecake mixture. In a medium bowl, beat cream cheese, sugar, egg yoke and vanilla extract until smooth with hand mixer. Beat until creamy with no lumps. Drop in dollops onto prepared brownie batter. Add the remaining Red Batter you reserved to go on top of cheesecake spoonfuls. Gently swirl the batters with a butter knife.
Bake for 30-35 minutes, until brownies and cheesecake are set. A brownie knife inserted into the cheesecake mixture should come out clean and the edges will be lightly browned. Do not overbake. Refrigerating the brownies will make cutting easier.
Cool in the pan completely before slicing and serving. You may want to save some for later, because they will be gone before you know it.