Whisk together the eggs, milk, caster sugar and salt in a flat dish.
Melt the butter in a large frying pan over medium heat.
Dip 2 slices white bread into the egg mixture, turning them over so they get completely coated.
Add them to the frying pan and sprinkle each one with a 1/4 of the chopped chocolate. Soak the remaining bread pieces in the egg mixture and set them atop the chocolate-slathered bread slices in the pan to make sandwiches. Press them down lightly with a spatula to seal their edges.
Fry for 3 minutes per side or until they are golden brown. Remove the sandwiches from the pan and serve immediately or keep them warm while you prepare the rest of the sandwiches. Serve the sandwiches dusted with the confectioners' sugar.