The trick for a perfect frittata is to cook over a medium to low heat and allow the mixture to set slowly without stirring. Stirring once the egg has begun to set will break the mixture apart. Too high a heat will burn the base before the egg is set sufficiently to finish in the oven or under the grill.
Parmesan cheese is not truly vegetarian, as it contains animal rennet. To make this dish 100% vegetarian, omit the cheese or find a suitable vegetarian substitute made without animal rennet. In supermarkets look for the 'parmesan style hard cheeses' which are suitable for vegetarians.