Make sure that all the ingredients are at room temperature.
Mix the softened butter with granulated sugar until it is pale and crystal-less. That should take about 5 minutes.
Then, add eggs one at a time and mix till well combined.
Mix buttermilk, vanilla, and red food coloring in one dish, and pour it into the bowl along with the other ingredients. The blend should be satiny, glossy, and semi-liquid.
Now, sift flour, cocoa, and baking powder into the mixture, spoon by spoon. Don’t mix it but fold it with a spatula until lumps disappear. The last step is adding the vinegar and folding it one last time. The batter is supposed to be a bit thick, but easy to pour out into the cake pan.
Baking
Preheat the oven to 360° F (180° C). Cover the ≈9-inch cake tin with the baking paper you previously wetted, so it’s easier to fit. Brush it lightly with cooking oil or butter and pour the batter in.
Bake it for about 15-20 minutes, depending on the thickness and oven. Check if it’s ready with a toothpick. Be careful not to overbake it.
Making the Cheese Cream
Mix together cream cheese, heavy cream, powdered sugar, vanilla, and cornstarch until smooth. Add eggs one at a time and mix just a bit more.
Lastly, add the juice of one lemon, plus you can also grate some peel for a more citrusy taste.
Divide a few spoons of the cream into one bowl and dye it with red food coloring. Add as much as you need to achieve the desired shade.
Assembling the Cake
Brush the dish with oil a bit so it doesn’t stick to the sides.
Crumble the baked cake and pour a bit of heavy cream or milk into it if needed. It should be moist and easy to press into the cake tin.
Now, pour the white cream and smash it lightly on the table a few times so the excess air bubbles disappear. Drizzle red cream spoon by spoon and swirl it a bit for a marbled look.
Final Baking
Bring your oven to 360 ° F (≈180° C) again. Pour water into one bigger baking dish to make a steam bath for your cake. Let it boil lightly.
Wrap the cake tin with aluminum foil just in case to prevent the water to come in touch with the cake. The water level shouldn’t go over half of the tin. Let it bake for 45 minutes. The middle will be jiggly a bit, so don’t worry, it will stiffen.
If you don't have a bigger dish for the steam bath, that's fine. Even though it helps to get a creamier texture, the cheesecake will bake even if you don't use it.
Let it cool for half an hour in the closed oven at first, then crack it open till the cake reaches room temperature. Let it cool in the fridge for 3 more hours at least, but best overnight.