Preheat the oven to 350 degrees. Grease with butter or cooking spray a 13x18 jelly roll pan and set aside.

In a large bowl, or the bowl of your stand mixer, add the flour, sugar, cocoa powder, salt, and baking powder. Stir to combine. In a small bowl add the eggs, oil, 2 tablespoons of milk, vanilla, food coloring, and white vinegar. Whisk the wet ingredient to combine. Make a well in the center of the dry ingredient and pour the wet ingredients into the center. Mix until well combine or with the cookie paddle attached, mix on medium-low speed until well combined. The batter will be very thick.

Remove about 3/4 of a cup of the batter and put it in a small bowl (or the bowl the wet ingredients just came out of) and set aside. Spread the rest of the batter in the bottom of the jelly roll pan.

To make the cheesecake layer combine the cream cheese and sugar in the bowl of your stand mixer and beat on medium speed until well combined and fluffy, about 3 minutes. Add the eggs and vanilla and beat another minute until well combined. Spread the cheesecake layer evenly on top of the red velvet layer in the pan.

Add the remaining 2 tablespoons of milk to the batter that you saved in the small bowl. Use a fork to whisk and combine it well. Drop the now thinned batter by small spoonfuls over the cheesecake layer and then use a toothpick to marble the cheesecake and thinned batter together. You just pull the toothpick across the top of the dessert with a bit of a swirling motion. Do this until it is marbled as much as you like.

-OR-

You can make little hearts on top! Do this by adding the thinned batter to a pastry bag with a small circle tip or in a ziplock bag (and you'll cut off a little tip of the corner). Drop the icing in small circles onto the top of the cheesecake layer. You have to work kind of fast because the batter is thin enough that it just drips out of the bag if you aren't moving pretty quick. Leave a little space in between the circles and it'll be easier to make the hearts if the circles are in a line. The size of the dots ranged from dime-sized to about half that. Pull the end of a toothpick from the top of the circle to the bottom to make a heart. The hearts will look best if you don't pick up the toothpick in between circles, just drag down the line.

Bake the bars for 28-30 minutes, rotating the pan half way through baking. Let the bars cool in the pan for 20 minutes before cutting. Store leftovers in an air-tight container in the fridge.

Notes: You don't have to cut it into hearts. It would make a lot of cute little squares.