Preheat oven to 350 degrees F.

Line a 9" square baking dish with aluminum foil (you will need 2 pieces overlapped to fully cover the bottom and sides of the pan with the ends folded over the edges of the pan) and spray lightly with cooking spray. *Note: I made mine in an 8" square pan and it was intense... it filled the entire pan (even with me not using quite all of the brownie batter) and then it threatened to overflow in the oven. So definitely use a 9" pan! And note that when using a 9" pan, the brownies will end up a bit shorter than mine shown in the photo above*

Place the chocolate and butter in a medium-sized saucepan. Heat over medium-low heat, stirring constantly, until completely melted and smooth.

Remove from heat and whisk in the sugar. *Note: Mixture will look grainy. It's ok, it's supposed to look like this.*

Transfer mixture to a large mixing bowl, then add in the eggs one at a time, beating with an electric mixer after each addition. *Note: beat the eggs in on medium/medium-high speed so they do not cook.*

Add the flour, food coloring, baking powder, salt, buttermilk, vanilla and vinegar and stir to combine (make sure everything is thoroughly combined, but try not to over-mix). *Note: I used my electric stand mixer fitted with the paddle attachment on low (stir) speed for this, but then still needed to mix a bit by hand because some of the batter that was on the bottom didn't mix in. Just make sure everything is thoroughly mixed before you pour into the pan, otherwise it won't all have the same red color.*

Pour 3/4 of the batter into the prepared baking dish (reserving the remaining 1/4 to be used later in the recipe) and then move on to making the cheesecake batter.

Beat the cream cheese with the sugar. (I did this in a small mixing bowl with my handheld electric mixer)

Add in the egg and vanilla and beat until thoroughly combined and mixture is completely smooth and creamy.

Pour the cheesecake batter over top of the brownie batter and spread out to cover the brownie batter in an even layer.

Drop the reserved brownie batter by spoonfuls over top of the cheesecake batter layer, then use a knife to swirl into the cheesecake batter.

Bake in the preheated oven for 15 minutes, then place a piece of foil loosely over top of the pan and continue baking for another ~30-40 minutes, until a toothpick inserted in the center comes out with just a few crumbs (no longer comes out with batter). *Note: The foil is necessary to avoid the cheesecake batter burning, but it needs to be laid loosely (preferably tented in the middle a bit) so it doesn't lay on top of the brownies or else the top of the brownies might stick to the foil.*

When done, remove from the oven and allow to cool to room temperature, then thoroughly chill in the refrigerator before slicing. (if you can't wait for them to be completely chilled, the only issue is that they won't cut as cleanly and they will taste a bit cakey, whereas after fully chilling they will have a more chewy consistency).

Store brownies in an air-tight container in the refrigerator.

When serving, you can eat these cold, room temperature or warmed up. When they're warmer, they have more of cakey consistency. When they're straight out of the refrigerator or have only sat out for about 10 minutes, they will have more of a chewy/fudgy consistency. Either way is delicious, which way you choose depends on what kind of brownie consistency you prefer.