Preheat the oven to 350°F. Grease a 9x13x2-inch baking dish or sheet pan.

In a mixing bowl, cream together the sugar and butter. Add in the eggs one at a time, mixing well in between additions. In a small bowl, mix together the cocoa powder and the food coloring. Mix into the butter mixture.

In another bowl, mix together the flour and salt. Add alternately with the buttermilk to the butter mixture. Stir in the vanilla. In a small bowl, mix together the baking soda and vinegar. Add to the mixture and mix well.

Pour mixture into the prepared baking dish. Bake in the preheated oven for 20-25 minutes, or until a toothpick inserted in the middle comes out clean. Remove and cool completely.

Once cool, cut the cake into 1-inch squares. Place on a baking sheet and bake for 10-15 minutes, or until slightly dried out.

Make the bread pudding mix: In a medium bowl, mix together the half-and-half, eggs, egg yolk, salt and vanilla. In the bowl of a stand mixer, or with a hand mixer in a medium bowl, mix together the cream cheese and powdered sugar until smooth. Stir in the half-and-half mixture.

Place the red velvet cake cubes in a large baking dish or in individual baking dishes. Pour the pudding mix over the cubes, making sure to soak with the mixture. Bake for about 30 minutes, or until the pudding is set. (Time will vary, depending on the size of your baking dish(es).) Serve sprinkled with powdered sugar or with ice cream.