Bring a large pot of water to a boil, add the eggs and boil for 7½ minutes, stirring slowly for the first minute. Drain the eggs, transfer immediately to a large bowl of iced water and allow to stand for 10 minutes until completely cool. Peel the eggs under running water, then slice them in half and separate the yolks and the whites.

Combine the yolks with the parmesan and mayonnaise and mash with a fork until the mix reaches a smooth consistency. Finely chop the egg whites and stir through the yolk mixture, then add the ham. Season well with salt and black pepper.

Cut the bread rolls vertically through the top of the roll, but not all the way to the base, so they can be opened up like a butterfly. Fill with the egg mixture, grind a little black pepper on top and serve.