Preheat oven to 350 degrees F.
Begin by making the cream cheese swirl. Combine room temperature cream cheese, vanilla extract, powdered sugar, egg, and flour to a medium bowl. Use an electric mixer or whisk to combine and mix until smooth. Set aside.
In a large bowl, mix together the dry ingredients - cocoa powder, all purpose flour, baking soda, baking powder, and kosher salt. Give it a good whisk and set aside.
Make the cake batter. Start by creaming together room temperature butter and vegetable oil in the bowl of a stand mixer fitted with the paddle attachment on medium speed. Mix for about 2-3 minutes then add sugar and continue to mix for another 2 minutes. Mixture may be a little soupy, this is OK/normal.
Begin adding eggs, one at a time while continuing to mix the cake batter. Then, pour in vanilla extract and vinegar.
Add the flour mixture into the batter, pour in buttermilk and mix until just combined. Then add the red gel food coloring and mix until the batter is red. Spray a 10-cup bundt cake pan with nonstick baking spray (I used Baker's Joy).
Pour ¾ of the batter into the prepared pan then gently spoon the cream cheese mixture on top of the batter. Add the remaining batter on top and bake for 55-65 minutes, until a toothpick comes out with a tiny bit of crumbs.
Allow the cake to cool in the bundt pan for 5 minutes, then turn over onto a wire rack / cooling rack. Let the cake cool completely.
Make the cream cheese glaze. Mix together room temperature cream cheese with butter, powdered sugar, and vanilla extract until smooth. Heat it in the microwave for about 30-45 seconds and drizzle all over the cake once the cake has cooled completely.