Preheat the oven to 150 degrees C. Put the kettle on.
In a large frying pan over medium high heat saute in butter the carrots, onion and parsley for a few minutes. Add the zucchini and cook for a further 15 minutes, stirring occasionally.
In a mixing bowl whisk the eggs then add the cream and Parmesan. Remove the zucchinis from the heat and add the egg mixture. Turn everything into a buttered baking dish.
To bake create a bain marie by laying a tea towel in the bottom of a large roasting tin or baking dish then place the smaller baking dish with the zucchinis on top of the towel. Place in the oven and carefully pour boiling water from the kettle halfway up the sides of the baking dish.