Preheat your grill to high. Heat a small, non-stick frying pan until medium hot. Dry fry the prosciutto until crisp. Remove to a plate, keep warm, and put the pan back on the heat.
Meanwhile, whisk the eggs in a small bowl and season with sea salt and pepper. Pour into the hot pan and, using a fork, mix the eggs around to cook a little. Scatter the tomatoes on the top, remove the pan from the heat and place under the hot grill, about 6–7cm away. Continue to cook until the eggs are just cooked and the tomatoes are warmed through.
To serve, place the prosciutto on top, sprinkle over the basil and chilli, if using. Season with black pepper and finish with a drizzle of olive oil, if you like.