Whisk the 2 large eggs together in a small bowl, set aside.
In a large bowl, mix butter with sugar, 2 tsp. vanilla extract, cocoa powder, salt, food coloring, and vinegar.
Fold in flour to the mixture above. Do NOT over mix.
Spray an 8 x 8 baking pan with non-stick spray. (don’t forget the sides)
Pour batter into pan, leaving a little extra in the bowl for later.
In a separate bowl combine cream cheese, sugar, egg yolk, and 1/2 tsp. vanilla extract using hand mixer on medium speed. Mix for about 1 minute until smooth.
Spoon dollops of the cheese cake filing on top of the brownie batter in the pan.
Pour extra brownie batter over the top of both layers.
Using a butter knife, start at the top of the pan and go through the batter and cheesecake filling from side to side across the pan. Once you have gone side to side all the way across, change directions and do the opposite.
Bake for 28-30 minutes. They are done when a toothpick poked in the center comes out clean.