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Special equipment: jumbo sized 6-cup muffin tin
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Heat the oven to 350 degrees F.
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In a food processor fitted with the grater attachment, push chunks of the potato through the chute to grate.
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Once all the potatoes are grated, put them into a piece of cheesecloth or a clean kitchen towel and squeeze to remove the moisture.
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Add the potatoes to a large bowl, stir in the melted butter and season well with salt and pepper, to taste.
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Spray the muffin tin lightly with nonstick cooking spray.
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Press the grated potatoes evenly into the muffin cups being sure the potatoes go up the sides and a thin layer and covers the bottom.
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Bake until the top edges turn light golden brown and the potatoes are cooked through, about 35 to 40 minutes.
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Meanwhile, in a small bowl toss together the prosciutto with maple syrup and a few grinds of freshly ground black pepper.
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Set aside.
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Remove the potatoes from the oven and gently crack an egg into each cup.
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Bake until the egg whites set but the yolk remains runny, about 6 to 8 minutes.
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Remove from the oven and set the oven to broil.
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Top the eggs with grated cheese and put the maple prosciutto on another sheet tray.
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Broil both until cheese melts, and prosciutto crisps slightly, about 1 minute.
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Top the eggs with crispy prosciutto and serve immediately.