Preheat oven to 350°F (175°C) and line an 8×8-inch baking pan with parchment paper.
In a mixing bowl, whisk together melted butter, granulated sugar, and brown sugar until smooth.
Mix in the egg, red food coloring, vanilla extract, and white vinegar.
In a separate bowl, sift together the flour, cocoa powder, salt, and baking powder.
Gradually add the dry ingredients to the wet mixture and stir until combined. Fold in 1/2 cup mini chocolate chips.
Spread 3/4 of the red velvet batter into the prepared pan.
In a new bowl, beat softened cream cheese, 1/4 cup sugar, egg yolk, and 1/2 teaspoon vanilla until smooth.
Spread the cheesecake mixture evenly over the red velvet layer.
Drop spoonfuls of the remaining red velvet batter on top of the cheesecake. Swirl gently with a knife or toothpick for a marbled effect.
Sprinkle the remaining 1/4 cup mini chocolate chips on top.
Bake for 30-35 minutes or until the center is set and a toothpick inserted comes out mostly clean.
Cool completely, then refrigerate for at least 2 hours before slicing into bars.