Line 4 ramekins with prosciutto so the bottom and sides are almost completely covered and some prosciutto drapes over the sides. Cut the prosciutto to fit better if necessary. Crack an egg into each prepared ramekin. Drizzle 1 tablespoon of half-and-half on top of each egg and sprinkle each with 1 tablespoon cheese. Season with pepper.
Arrange the ramekins in a 9-inch square baking pan and carefully pour in the boiling water until it reaches halfway up the ramekins.
Bake for 10 to 12 minutes, or until the whites are set and the yolk is done almost to the desired firmness. The eggs will continue to cook after you remove them from the oven, so under bake them slightly.
Serve immediately. Eat the eggs right out of the ramekins with a knife and fork.