Put the chicken breasts between 2 sheets of oiled clingfilm and beat with a rolling pin until almost doubled in size. Place the beaten egg on a plate and the breadcrumbs on a separate plate. Lightly coat each chicken breast in egg and then in the breadcrumbs. Set aside.
Heat the oil in a large, heavy-based frying pan. (You may need to use 2 pans so that you can cook all the chicken at the same time.) Cook the chicken over a moderate heat for 4 minutes on each side or until golden and crisp.
Transfer to 2 baking sheets and and top with Gruyère cheese slices and a slice of prosciutto. Grill under a hot preheated grill for 2 minutes, then turn off the heat and leave to stand for a further 2 minutes or until the cheese has melted a little. Serve garnished with sage leaves.