Preheat the oven to 350 degrees F.
Line a 9 x 9-inch square baking dish with two pieces of aluminum foil, folding ends over the edges. Spray with cooking spray.
Combine the chocolate and butter in a large, microwave safe bowl. Cook 30 seconds at a time until melted, stirring well after each time. Whisk in the sugar.
One at a time, add the eggs, whisking well between each addition. Stir in the flour, food coloring, baking powder, salt, buttermilk, vanilla, and vinegar. Combine well, then pour into the prepared baking dish.
In the bowl of a stand mixer fitted with a paddle attachment, beat the cream cheese, sugar, vanilla, and egg yolk. Drop spoonfuls over the brownie batter, then use a table knife to swirl into the batter.
Bake 40-50 minutes, or until a toothpick inserted into the center comes out with just a few crumbs attached. Allow to cool completely before slicing.