Break the woody ends off the asparagus and discard. Toss the spears in 1 tablespoon of the olive oil.
Heat a griddle pan until hot and cook the asparagus for 4–5 minutes, until starting to look a little charred. Cut the asparagus spears into thirds.
Beat the eggs in a large bowl with the grated Parmesan, oregano and some salt and pepper. Add the asparagus.
Heat the remaining oil in a flameproof, nonstick frying pan. Pour the mixture into the pan and cook for 8–10 minutes over a low heat, tipping the pan from time to time to allow the runny egg to reach the edges to cook.
Cook for a further 4–5 minutes under a preheated hot grill, until the top is golden.
Turn out on to a board, cut into wedges and serve immediately.