Peel the eggplants and cut off the tips. Cut each eggplant horizontally into two to three portions.
Arrange the eggplants side by side on a plate then wrap the plate with cling film. Remember to leave a vent for steam to escape.
Microwave the eggplants for two minutes (we have a 1000W microwave oven; if the wattage of your microwave is different, you will need to adjust the cooking time).
Peel off the cling wrap and let the eggplants cool a bit.Butterfly the eggplants. Split each piece of eggplant vertically without cutting all the way through.
Open up the split eggplants then make vertical cuts along the length of the left and right sides.
Sprinkle the butterflied eggplants with salt and pepper.
Dredge each butterflied eggplant in flour, dip in egg then coat thoroughly with panko.
In a frying pan heat enough cooking oil to reach a depth of one inch.
Fry the breaded eggplants, in batches if your frying pan is on the small side, over medium heat until the coating is golden and crisp, and flipping them over for even cooking.
Move the eggplants to a rack as they cook.
Preheat the oven to 400F using the broiler (top heasetting.
Arrange the fried eggplants on a baking tray and top each with mozzarella.
Broil the eggplants just until the cheese melts.
Sprinkle Parmesan and parsley over the cheese-y eggplant katsu before serving.