Preheat the oven to 375°F. 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 Tbs. half-and-half on top of each egg and sprinkle each with 1 Tbs. cheese. Season with pepper.
Arrange the ramekins in a 9-inch square baking pan and carefully pour 4 cups boiling water into the pan until it reaches halfway up the ramekins.
Bake for 10 to 12 minutes, or until the whites are set and the yolk is done to the desired firmness. The eggs will continue to cook after you remove them from the oven, so underbake them slightly. Serve immediately. Eat the eggs right out of the ramekins with a knife and fork.