Preheat oven to 375 degrees.
In a deep cast iron pan, saute fiddleheads, chopped potatoes, and diced shallots, in a generous amount of butter, olive oil, or bacon fat. Cook over medium-low heat until fiddleheads are fiddleheads and potatoes are tender, and shallots are getting translucent - about 15-20 minutes.
Whisk together eggs and cheese in a large bowl, then add to the pan with the fiddlehead mixture. If you'd like to skip dirtying a bowl, just add the cheese and eggs directly to the pan, mixing vigorously as you crack in each egg.
Stir everything well so that it's thoroughly mixed, then put the whole thing in the oven. Bake until the center is set, and frittata is golden brown - about 35 minutes.
Cool slightly, and serve.