, the way that I make Frittata is to finish the dish in a 350° oven until just done ... 8-20 minutes depending on the size.
Keep an eye on it as to not over bake the eggs, this will make for a very dry dish.
Think of Frittatas as a crust-less quiche, you want the eggs to be soft and moist not dry and sponge-y.
Another method if you do not have an oven-proof pan is to utilize a large dinner plate.
Place the plate over the pan, with one hand flat over it and holding firmly; flip the entire pan, Frittata and all, onto it.
Then gently slide the un-cooked top of the eggs to the hot surface of the pan.
Again, keep an eye on it, you don't want to over cook it.