Finely slice the onion and the pepper.
Heat the oil in an ovenproof frying pan and gently sauté the onion.
Finely slice the mushrooms and add these to the pan together with the pepper slices. Sauté under cover for 5 minutes then add the tomatoes. Cover and cook for another couple of minutes.
Mix the eggs lightly with 1 Tbsp of the grated cheese and half of the coriander. Pour this mixture over the vegetables and cook gently, under cover, until the egg has just set in the middle.
Sprinkle the remaining grated cheese and put the pan in the oven to brown the top of the frittata, using the grill.
Serve with freshly ground peppercorn and coriander leaves scattered over the top.