Preheat the oven to 180 C / Gas 4. Prepare a baking dish by brushing it with butter and set it aside.
Meanwhile, pour 2.5cm (1 in) of water in a large saucepan and bring to the boil. Once boiling, add the asparagus, onion and pepper. Stir and continue to boil for 1 to 2 minutes.
Reduce the heat, cover and simmer until all of the vegetables are cooked and they are crisp but tender. Turn off the heat and drain all the liquid. Layer the vegetables including the courgette in the buttered baking dish. Make sure to reserve some of the asparagus spears as you will need them to garnish the dish.
In a bowl combine the eggs, light cream and fresh parsley. Season it with some salt and black pepper and mix. Pour this over the arranged vegetables in the baking dish.
Bake uncovered for 30 minutes. Insert a knife at the centre of the dish and if it comes out clean, your frittata is ready. Let it stand for 10 minutes and garnish with some of the asparagus spears you have reserved for serving.