Make the red velvet batter: In a large mixing bowl, combine the flour, granulated sugar, cocoa powder, baking soda and salt. Whisk to combine. In the bowl of an electric mixer combine the vegetable oil, butter, sour cream and eggs. Mix well. Add the food color, vanilla and vinegar. Mix again. Add the flour mixture to the creamed mixture until just combined. Scrape down the bowl and fold in any streaks of flour or butter by hand using the spatula.
Make the cream cheese batter: Combine all ingredients in the bowl of an electric mixer. Beat until combined and no lumps of cream cheese remain.
Preheat the oven to 350°F.
Generously coat a 10-15 cup bundt pan with flour-based baking spray (such as Baker’s Joy). Spread 3 cups of batter into the prepared pan. Pour the cream cheese mixture on top; spoon the remaining red velvet batter evenly over the top. Bake about 1 hour 10 minutes, or until the top of the cake is cracked and a toothpick tester comes out clean. Transfer the cake to a wire rack to let cool in the pan 15 minutes. Turn the cake onto a serving plate or cake stand and let cool.
Make the glaze: Whisk together the confectioners’ sugar, salt and 2 tablespoons of milk in a medium bowl. If the mixture is thick, whisk in a little more milk or cream. The glaze should be thick but still of pouring consistency.
When the cake is cool, pour the glaze on top of the cake. Let stand until the glaze is set, about 30 minutes.
Store the cake covered in plastic wrap or in an air-tight cake keeper in the refrigerator. Bring the cake to room temperature before serving.