Warm 2 tablespoons of the olive oil in a frying pan over a medium heat. Add the spring onions, mushrooms and red peppers and cook and stir until tender, about 6 to 8 minutes. Remove from the pan and set aside.
Add the remaining 2 tablespoons olive oil to a large, oven-proof skillet with rounded sides. Arrange the potatoes in an overlapping circle starting in the middle, circling out. It's best to overlap the rows by about 1cm (1/2 in), but the plan here is to keep this layer as thin as possible. Cook the potatoes over a medium heat until they are tender and slightly brown.
In a bowl, beat together the eggs, water, salt and pepper. Stir in the spring onions, mushrooms and peppers. Pour the egg mixture over the potatoes, maintaining a medium heat. Cook for 5 minutes and sprinkle the cheese on top. Continue to cook for 5 more minutes until the first 12cm (5 in) of the outside edges of the frittata are set.
Bake in the preheated oven for 15 minutes until the centre is set. Remove from the oven and allow to cool for 10 minutes.
To serve, place a large plate over the top of pan and in one smooth movement flip both over together. The frittata should fall out onto the plate revealing a lovely, crispy crust of potatoes. Slice and serve.
I use a mandolin to slice the potatoes - very handy. This is great served cold.