Cook the potatoes in a pan of boiling water with the mint sprig for 10-15 minutes until tender. Drain and, when cool enough to handle, cut into thick slices.
Meanwhile, heat the butter in a large frying pan. When the butter is bubbling, add the courgettes and cook for 5 minutes, stirring. Add the frozen peas to the pan after 2 minutes. When the 5 minutes are up, remove the pan from the heat and stir in the mint and sliced potatoes. Tip this mixture into a buttered 27cm x 16.5cm (4cm deep) roasting tray, the base lined with baking parchment.
Beat the eggs in a bowl and stir in the Cheddar with a little black pepper. Pour over the courgettes and potatoes. Sprinkle over the parmesan. Bake for 20-25 minutes, until the egg has set. Allow to cool for 10 minutes. Use a palette knife to go round the edges, then remove from the tin and discard the baking parchment.