Creating Marbled Red Velvet Cheesecake Bars can be a rewarding and breezy process if you follow these steps:

1. Preheat Oven: Preheat your oven to 350°F (175°C). Grease a 9×9-inch baking pan or line it with parchment paper for easy removal.

2. Mix Dry Ingredients: In a large mixing bowl, whisk together the flour, sugar, baking powder, baking soda, salt, and cocoa powder.

3. Combine Wet Ingredients: In another bowl, beat together the vegetable oil, egg, buttermilk, red food coloring, vanilla extract, and white vinegar until well blended.

4. Combine Mixtures: Gradually add the wet ingredients to the dry ingredients, stirring until just combined. Do not overmix.

5. Prepare Cheesecake Layer: In a separate bowl, beat the softened cream cheese until smooth. Add in the granulated sugar and vanilla extract, then mix until fully combined. Beat in the eggs one at a time until smooth.

6. Layer the Mixtures: Pour half of the red velvet batter into the prepared pan. Then, spoon the cheesecake layer evenly over it. Finally, drop spoonfuls of the remaining red velvet batter on top of the cheesecake layer. Use a knife to swirl them together for the marbled effect.

7. Bake the Bars: Bake in the preheated oven for 40-45 minutes, or until a toothpick inserted in the center comes out clean. Allow to cool in the pan for 30 minutes before transferring to a wire rack to cool completely.