Make 4 sandwiches with the bread slices and ham, then dip them in the milk. Place on a plate and lightly weigh down with another plate. Leave for 15 minutes.
Place the eggs in a shallow bowl and dip the sandwiches into the egg. Heat a little of the oil in a frying pan, add the sandwiches in batches and cook for 3–5 minutes until golden all over, adding more oil as necessary.
Cut into quarters, then transfer to serving plates and serve sprinkled with the paprika.