Cut each piece of chicken in half horizontally, keeping the edges together, and place each piece between 2 sheets of plastic wrap. Using a pan, pound out to thin the chicken.
Place the chicken pieces on a baking sheet and sprinkle with salt and pepper. Arrange one slice of cheese and one slice of ham on each half of the chicken. Fold the other half of the chicken on top, making sure the ham and cheese are well tucked into the chicken.
Beat the eggs with the milk and add the nutmeg, salt and pepper. Dip a chicken breast in the flour, then in the egg mixture and finally in the breadcrumbs. Repeat with all the chicken breasts.
Heat olive oil in a large frying pan over medium to high heat. Place chicken in pan and cook 2 minutes on each side. Transfer to a tray lined with baking sheet and place in oven for 20 minutes at 180°C. Serve immediately and enjoy with a green salad.