Preheat your panini press to high.
Place the flour, egg, and panko each into separate, shallow bowls. Whisk the egg slightly to blend it together. Season each piece of chicken with salt and pepper, and then coat each piece in flour, egg, and panko, in that order. Set the breaded chicken aside.
Heat a few tablespoons of olive oil in a large skillet over medium heat and add the chicken. Cook until the chicken is cooked through and golden and crispy on each side, about 4 minutes per side. Remove the cooked chicken from the pan and set aside.
To make the panini, take the ciabatta rolls and slice them in half lengthwise. Butter the top and bottom of each roll, yes the OUTside. Next spread a little mustard on the bottom half of each roll, the inside of the bottom half. Layer on the cheese and ham by placing a slice of cheese on both the bottom and top pieces, and a piece of ham on just the bottom. Next, place a piece of chicken on the bottom half of each sandwich. Top the sandwiches and move to the panini press.
Pressing down on the panini press, grill until the sandwiches are golden brown and the cheese is melted, about five minutes. Serve warm, and enjoy!