Preheat the oven to 350 degrees F. Greased 9 by 13 by 2-inch sheet pan.
In a mixing bowl, cream the sugar and butter, beat until light and fluffy. Add the eggs 1 at a time and mix well after each addition. Mix cocoa and food coloring together and then add to sugar mixture; mix well. Sift together flour and salt. Add flour mixture to the creamed mixture alternately with buttermilk. Blend in vanilla.
In a small bowl, combine baking soda and vinegar and add to mixture. Pour batter into the prepared sheet pan. Bake for 20 to 25 minutes or until a toothpick inserted into the center comes out clean. Remove from heat and cool completely. When the cake is cooled, cut into 1-inch cubes.
Place cubes onto 11 by 17-inch cookie sheet. Place in oven for 10 minutes.
Combine the half-and-half, eggs, egg yolk, salt, and vanilla in a medium bowl. With an electric hand mixer in a large bowl, beat the cream cheese and sugar until smooth. Mix in the half-and-half mixture.
Place the red velvet cubes in a large baking dish or 8 individual ramekins. Add the pudding mixture to the dish. Make sure the cake cubes are completely covered. Bake for about 30 minutes, or until the pudding is set. Serve with ice cream.