Peel and wash the potatoes. Either using a hand grater or in a food processor fitted with the grater attachment, push chunks of the potato through the chute to grate. Once all the potatoes are grated, put them into a piece of cheesecloth or a clean kitchen towel and squeeze to remove the moisture. Melt the butter and place in a large bowl. Stir in the potatoes and season well with salt and freshly ground black pepper, to taste.
Using either a small knob of butter or non-stick cooking spray, lightly grease a jumbo sized (6 case) cake tin (muffin pan). Press the grated potatoes evenly in a thin layer around the muffin cups being sure to cover the sides and bottom. Bake in a preheated moderate oven (Mk 4 - 350ºF - 180ºC) for about 35 - 40 minutes until the top edges of the potato turn light golden brown and the potatoes are cooked through.
Meanwhile, roughly chop the prosciutto (Parma ham) and, in a small bowl, toss together the prosciutto with maple syrup and a few grinds of freshly ground black pepper. Set aside. Grate (shred) the cheese and set aside.
Remove the potatoes from the oven and gently crack an egg into each cup. Return to the oven and bake for about 6 - 8 minutes until the egg whites set but the yolk remains runny.
Remove from the oven and set the oven to grill (broil). Top the eggs with grated cheese and put the maple prosciutto on another baking sheet. Grill (broil) both for 1-2 minutes until the cheese melts and the prosciutto becomes slightly crisp.
Remove from the oven, top the eggs with the crispy prosciutto and serve immediately.