Heat the oil in a large frying pan over a moderate heat. Cook the potatoes for 7–8 minutes, tossing occasionally.
Add the asparagus and 1/3 cup of water, sprinkle with salt, cover and steam for 10–12 minutes, or until the asparagus and potatoes are tender.
Meanwhile, whisk together the eggs, tarragon and parmesan with 1 tablespoon of water and a little freshly ground black pepper in a large bowl.
Preheat the grill to a moderate heat. Pour the egg mixture into the pan and swirl it around to cover the vegetables. Cook gently for 4–5 minutes until the eggs are almost set, shaking the pan from time to time.
Place the pan under the grill and cook for 2 minutes, or until the top looks set. Cut into wedges and serve hot or cold.