Put about four inches of oil or shortening into a good-sized pot (such as a Dutch oven).
Heat the oil/shortening to 350ºF. While that is heating up, cut a small pocket (about 1 inch in length) in the side of each bread slice.
In a small bowl, mix the cinnamon and sugar, then set aside. In a bowl larger than your piece of bread, mix the egg, milk, and vanilla, then also set aside.
Place each piece of stuﬀed bread into the bowl with egg mixture and allow it to soak for a few seconds. Place soaked bread into the hot oil/shortening and fry on both sides until lightly browned. When done, remove from oil and place on a plate lined with paper towels or a wire rack. Sprinkle with cinnamon sugar before serving.