In a medium bowl, beat cream cheese, sugar, egg, and vanilla extract until smooth and creamy.

Set aside while preparing the cake batter.

In a large bowl, whisk together flour, granulated sugar, cocoa powder, and baking soda.

In a separate bowl, whisk together vegetable oil, buttermilk, vanilla extract, eggs, red food coloring, and vinegar until fully combined.

Gradually add the wet ingredients to the dry ingredients, stirring until the batter is smooth and well-mixed.

Grease a bundt pan thoroughly to prevent sticking.

Pour one-third of the cake batter into the prepared pan.

Spoon half of the cheesecake mixture over the batter.

Add another third of the batter, followed by the remaining cheesecake mixture.

Finish with the final third of the batter, ensuring the cheesecake layer is fully covered.

Preheat oven to 350°F (175°C).

Bake for 38-43 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes, then invert onto a wire rack to cool completely.

In a small bowl, whisk together powdered sugar, milk, and vanilla extract until smooth.

Adjust consistency by adding more milk for a thinner glaze or powdered sugar for a thicker glaze.

Drizzle the glaze over the cooled bundt cake.

Add sprinkles for a festive touch if desired.