Cook the broad beans in a pan of boiling, salted water for 2-3 minutes, or until tender. Drain well, then refresh in cold water. When the beans are cool enough to handle, peel away the outer skins, if you want to.
Heat the oil in a small ovenproof frying pan over a low heat. Add the onion and season with a pinch of salt. Fry for 8-10 minutes, or until softened but not browned.
Meanwhile, preheat the grill to its highest setting. In a bowl, whisk the eggs until well combined and full of air, then season, to taste, with salt and freshly ground black pepper.
When the onions have softened, increase the heat to medium and pour in the beaten eggs. Sprinkle over the crumbled feta, mint leaves (if using) and cooked broad beans. Leave the pan on the heat for 2-3 minutes, or until the underside of the egg mixture is pale golden-brown. (NB: Do not stir the mixture.)
Transfer the pan to the grill and cook for a further 2-3 minutes, or until the top side of the egg mixture is firm and pale golden-brown. Place a large plate upside-down over the pan, then turn the pan over so that the omelette falls onto the plate. Cut it into wedges and serve with crusty white bread.