Preheat oven to 190°c and grease four 180ml ramekins.
Heat the oil in a medium frying pan; gently cook the prosciutto and mushrooms, stirring, until the mushrooms soften.
Add the onion, and stir continuously until they soften - a minute or so. Remove the pan from heat, and stir in half the cheese. Divide the prosciutto mixture among the ramekins and break two eggs into each dish. Bake uncovered for 5 minutes.
Remove from the oven briefly and quickly sprinkle the remaining cheese over the eggs, and return to the oven for a further 8 - 10 minutes or until the eggs set and the cheese melts.
Serve immediately with freshly ground black pepper, if desired.